In this paper, we introduce a novel variational framework rooted in algebraic geometry for the an... more In this paper, we introduce a novel variational framework rooted in algebraic geometry for the analysis of the Hardy Z-function. Our primary contribution lies in the definition and exploration of ∆ n (a), a newly devised discriminant that measures the realness of consecutive zeros of Z(t). Our investigation into ∆ n (a) and its properties yields a wealth of compelling insights into the zeros of Z(t), including the corrected Gram's law, the second-order approximation of ∆ n (a), and the discovery of the G-B-G repulsion relation. Collectively, these results provide compelling evidence supporting a new plausibility argument for the Riemann hypothesis.
In his foundational book, Edwards introduced a unique "speculation" regarding the possible theore... more In his foundational book, Edwards introduced a unique "speculation" regarding the possible theoretical origins of the Riemann Hypothesis, based on the properties of the Riemann-Siegel formula. Essentially Edwards asks whether one can find a method to transition from zeros of Z 0 (t) = cos(θ(t)), where θ(t) is Riemann-Siegel theta function, to zeros of Z(t), the Hardy Z-function. However, when applied directly to the classical Riemann-Siegel formula, it faces significant obstacles in forming a robust plausibility argument for the Riemann Hypothesis. In a recent work, we introduced an alternative to the Riemann-Siegel formula that utilizes series acceleration techniques. In this paper, we explore Edwards' speculation through the lens of our accelerated approach, which avoids many of the challenges encountered in the classical case. Our approach leads to the description of a novel variational framework for relating zeros of Z 0 (t) to zeros of Z(t) through paths in a high-dimensional parameter space Z N , recasting the RH as a modern non-linear optimization problem.
In this dissertation we study applications of methods of symplectic topology, mainly the theories... more In this dissertation we study applications of methods of symplectic topology, mainly the theories of Floer and quantum homology, to the following two subjects in complex projective geometry: (1) Morse-Bott degenerations of Kähler Manifolds and (2) manifolds with small dual. (1) Morse-Bott degenerations: A Morse-Bott degeneration is a holomorphic map π : X → D from a Kähler manifold (X, Ω) to the unit disc D ⊂ C such that Crit(π) ⊂ π−1(0) and the holomorphic Hessian of π is a a non-degenerate quadratic form when restricted to the normal bundle of Crit(π) in X. Our first result on the subject is showing that Lagrangian submanifolds in the singularity locus of the degeneration L ⊂ Crit(π) ⊂ Σ0 give rise to Lagrangian submanifolds Nz(L) in Σz = π −1(z) in the smooth fibers z 6= 0. Moreover, Nz(L) ⊂ Σz is topologically a sphere bundle over L. This could be seen as a generalization of the well known result stating that fibers of a Lefschetz fibration admit Lagrangian spheres corresponding...
r i=1 O P s (a i)) be a Fano projective bundle over P s and denote by Crit(X) ⊂ (C *) n the solut... more r i=1 O P s (a i)) be a Fano projective bundle over P s and denote by Crit(X) ⊂ (C *) n the solution scheme of the Landau-Ginzburg system of equations of X. We describe a map E : Crit(X) → P ic(X) whose image E = {E(z)|z ∈ Crit(X)} is the full strongly exceptional collection described by Costa and Miró-Roig in [15]. We further show that Hom(E(z), E(w)) for z, w ∈ Crit(X) can be described in terms of a monodromy group acting on Crit(X).
For a toric Fano manifold X denote by Crit(X) ⊂ (C *) n the solution scheme of the Landau-Ginzbur... more For a toric Fano manifold X denote by Crit(X) ⊂ (C *) n the solution scheme of the Landau-Ginzburg system of equations of X. Examples of toric Fano manifolds with rk(P ic(X)) ≤ 3 which admit full strongly exceptional collections of line bundles were recently found by various authors. For these examples we construct a map E : Crit(X) → P ic(X) whose image E = {E(z)|z ∈ Crit(X)} is a full strongly exceptional collection satisfying the Maligned property. That is, under this map, the groups Hom(E(z), E(w)) for z, w ∈ Crit(X) are naturally related to the structure of the monodromy group acting on Crit(X).
In 1970, based on newly available empiric evidence, a remarkable monotonicity property for |ζ(z)|... more In 1970, based on newly available empiric evidence, a remarkable monotonicity property for |ζ(z)| was conjectured by R. Spira. The ζ-monotonicity property can be written as follows: |ζ(x 2 + yi)| < |ζ (x 1 + yi) | for any x 1 < x 2 ≤ 0.5 and 6.29 < y. In this work we present an experimental study of the monotonicity conjecture, in the course of which new properties of ζ(z) are discovered. For instance, the spectrum of semilimits λ(z) ⊂ R and the core function C(z), which serves as a non-chaotic simplification of ζ(z) to the left of the critical line
We show that the existence of a non-trivial solution of x n + y n = p n , with p a prime number, ... more We show that the existence of a non-trivial solution of x n + y n = p n , with p a prime number, is equivalent to the existence of a solution of a certain (over-determined) system of (n − 1)-recursion relations ("zipper" equations) in Z p−1 .
Let X be a toric Fano manifold and denote by Crit(f X) ⊂ (C *) n the solution scheme of the corre... more Let X be a toric Fano manifold and denote by Crit(f X) ⊂ (C *) n the solution scheme of the corresponding Landau-Ginzburg system of equations. For toric Del-Pezzo surfaces and various toric Fano threefolds we define a map L : Crit(f X) → P ic(X) such that E L (X) := L(Crit(f X)) ⊂ P ic(X) is a full strongly exceptional collection of line bundles. We observe the existence of a natural monodromy map M : π 1 (L(X) \ R X , f X) → Aut(Crit(f X)) where L(X) is the space of all Laurent polynomials whose Newton polytope is equal to the Newton polytope of f X , the Landau-Ginzburg potential of X, and R X ⊂ L(X) is the space of all elements whose corresponding solution scheme is reduced. We show that monodromies of Crit(f X) admit non-trivial relations to quiver representations of the exceptional collection E L (X). We refer to this property as the Maligned property of the maps L : Crit(f X) → P ic(X). We discuss possible applications of the existence of such Maligned exceptional maps to various aspects of mirror symmetry of toric Fano manifolds.
For X = P n the Euler sequence is given by 0 → Ω 1 P n → O n+1 P n (−1) → O P n → 0 We describe t... more For X = P n the Euler sequence is given by 0 → Ω 1 P n → O n+1 P n (−1) → O P n → 0 We describe the Lagrangian cobordism corresponding to this sequence via mirror symmetry, in the sense of Biran-Cornea. In particular, we describe the mirror Lagrangian of the cotangent sheaf Ω 1 P n ∈ D b (P n) in the mirror Fukaya category F uk(U ∆).
We study smooth projective varieties with small dual variety using methods from symplectic topolo... more We study smooth projective varieties with small dual variety using methods from symplectic topology. For such varieties we prove that the hyperplane class is an invertible element in the quantum cohomology of their hyperplane sections. We also prove that the affine part of such varieties are subcritical. We derive several topological and algebraic geometric consequences from that. The main tool in our work is the Seidel representation associated to Hamiltonian fibrations.
For $N \in \mathbb{N}$ consider the $N$-th section of the approximate functional equation $$ \zet... more For $N \in \mathbb{N}$ consider the $N$-th section of the approximate functional equation $$ \zeta_N(s)= \sum_{n =1 }^N B_n(s),$$ where $$ B_n(s)= \frac{1}{2} \left [ n^{-s} + \chi(s) \cdot n^{s-1} \right ].$$ Our aim in this work is to introduce a new approach for the Riemann hypothesis by studying the way pairs of consecutive zeros of $\zeta_N(s)$ change with respect to $N$. For the initial stage, it is known that the non-trivial zeros of $\zeta_1(s)$ all lie on the critical line $Re(s)=\frac{1}{2}$. In the region $2N \leq Im(s) \leq 2 \pi (N+1)$ the function $\zeta_N(s)$ serves as an approximation of $\zeta(s)$ itself, and it was conjectured by Spira that in this region $\zeta_N(s)$ also admits zeros only on the critical line. We show that the appearance of zeros of a section off the critical line can be realized as the result of two consecutive zeros meeting and pushing each other off the critical line as $N$ changes, a process to which we refer to as a collision of zeros. Based...
We show that the existence of a non-trivial solution of $x^n+y^n=p^n$, with $p$ a prime number, i... more We show that the existence of a non-trivial solution of $x^n+y^n=p^n$, with $p$ a prime number, is equivalent to the existence of a solution of a certain (over-determined) system of $(n-1)$-recursion relations ("zipper" equations) in $\mathbb{Z}_{p-1}$.
Our aim in this work is to present a modern study of the classical Riemann zeta function aided by... more Our aim in this work is to present a modern study of the classical Riemann zeta function aided by contemporary computational tools. One of our main discoveries in this work regarding $\zeta(z)$ is the observation of the following natural property (alongside various other new properties): $$ \vert \zeta (0.5 + y i ) \vert < \vert \zeta \left ( x+y i \right )\vert \hspace{0.5cm} \textrm {for all } \hspace{0.25cm} 0 \leq x<0.5 \textrm{ and } 6.29<y<Y,$$ with $0<<Y$ (we conjecture that $Y=+\infty$). In particular, the Riemann hypothesis is a direct consequence of the above property (in any domain which it holds) which gives a natural explanation to the fact that $\zeta(z)$ admits no zeros in the critical strip with $Re(z) \neq 0.5$.
Let X be a toric Fano manifold given by a reflexive polytope Δ and let Crit(f)⊂(C*)s be the solut... more Let X be a toric Fano manifold given by a reflexive polytope Δ and let Crit(f)⊂(C*)s be the solution scheme of the Landau–Ginzburg system associated with a Laurent polynomial fu(z)≔∑n∈Δ◦(0)∩Zsunzn∈L(Δ◦). Motivated by mirror symmetry, we construct a map E : Crit(fu) → Pic(X) and show various cases of (X, fu) for which its image Eu(X)≔E(z)|z∈Crit(fu)⊂Pic(X) is a full strongly exceptional collection of line bundles. Moreover, we study relations between Hom(E(z), E(w)) for z, w ∈ Crit(fu) and the structure of the monodromy group acting on Crit(fu). The construction relies on a study of the tropical and co-tropical properties of Crit(fu) as log|u| → ±∞.
Fermat, about 1637, stated that Itlt is impossible to separate a cube into two cubes, or a biquad... more Fermat, about 1637, stated that Itlt is impossible to separate a cube into two cubes, or a biquadrate into two biquadrates, or in general any power higher than the second into two powers of like degree; I have discovered a truly remarkable proof which (JJ this margin is too small to contain. 1t This theorem is known as Fermat's Last Theorem. This problem may be more simply stated by
Let X be a toric Del-Pezzo surface and let Crit(W) ⊂ (C *) n be the solution scheme of the Landau... more Let X be a toric Del-Pezzo surface and let Crit(W) ⊂ (C *) n be the solution scheme of the Landau-Ginzburg system of equations. Denote by X • the polar variety of X. Our aim in this work is to describe a map L : Crit(W) → F uk trop (X •) whose image under homological mirror symmetry corresponds to a full strongly exceptional collection of line bundles.
Let X be a toric Fano manifold and denote by Crit(f X) ⊂ (C *) n the solution scheme of the corre... more Let X be a toric Fano manifold and denote by Crit(f X) ⊂ (C *) n the solution scheme of the corresponding Landau-Ginzburg system of equations. For toric Del-Pezzo surfaces and various toric Fano threefolds we define a map L : Crit(f X) → P ic(X) such that E L (X) := L(Crit(f X)) ⊂ P ic(X) is a full strongly exceptional collection of line bundles. We observe the existence of a natural monodromy map M : π 1 (L(X) \ R X , f X) → Aut(Crit(f X)) where L(X) is the space of all Laurent polynomials whose Newton polytope is equal to the Newton polytope of f X , the Landau-Ginzburg potential of X, and R X ⊂ L(X) is the space of all elements whose corresponding solution scheme is reduced. We show that monodromies of Crit(f X) admit non-trivial relations to quiver representations of the exceptional collection E L (X). We refer to this property as the Maligned property of the maps L : Crit(f X) → P ic(X). We discuss possible applications of the existence of such Maligned exceptional maps to various aspects of mirror symmetry of toric Fano manifolds.
Proceedings of the American Mathematical Society, 2014
Morse-Bott fibrations generalize the class of Lefschetz fibrations, allowing for non-isolated sin... more Morse-Bott fibrations generalize the class of Lefschetz fibrations, allowing for non-isolated singularities. A Morse-Bott degeneration is a Morse-Bott fibration π : X → D whose only singular value is 0 ∈ D. We show that Morse-Bott degenerations with Crit(π) = CP k for 0 < k admit restrictions which are unique to the non-isolated case. These restrictions are obtained as an application of methods of Floer homology for monotone Lagrangian submanifolds.
In this paper, we introduce a novel variational framework rooted in algebraic geometry for the an... more In this paper, we introduce a novel variational framework rooted in algebraic geometry for the analysis of the Hardy Z-function. Our primary contribution lies in the definition and exploration of ∆ n (a), a newly devised discriminant that measures the realness of consecutive zeros of Z(t). Our investigation into ∆ n (a) and its properties yields a wealth of compelling insights into the zeros of Z(t), including the corrected Gram's law, the second-order approximation of ∆ n (a), and the discovery of the G-B-G repulsion relation. Collectively, these results provide compelling evidence supporting a new plausibility argument for the Riemann hypothesis.
In his foundational book, Edwards introduced a unique "speculation" regarding the possible theore... more In his foundational book, Edwards introduced a unique "speculation" regarding the possible theoretical origins of the Riemann Hypothesis, based on the properties of the Riemann-Siegel formula. Essentially Edwards asks whether one can find a method to transition from zeros of Z 0 (t) = cos(θ(t)), where θ(t) is Riemann-Siegel theta function, to zeros of Z(t), the Hardy Z-function. However, when applied directly to the classical Riemann-Siegel formula, it faces significant obstacles in forming a robust plausibility argument for the Riemann Hypothesis. In a recent work, we introduced an alternative to the Riemann-Siegel formula that utilizes series acceleration techniques. In this paper, we explore Edwards' speculation through the lens of our accelerated approach, which avoids many of the challenges encountered in the classical case. Our approach leads to the description of a novel variational framework for relating zeros of Z 0 (t) to zeros of Z(t) through paths in a high-dimensional parameter space Z N , recasting the RH as a modern non-linear optimization problem.
In this dissertation we study applications of methods of symplectic topology, mainly the theories... more In this dissertation we study applications of methods of symplectic topology, mainly the theories of Floer and quantum homology, to the following two subjects in complex projective geometry: (1) Morse-Bott degenerations of Kähler Manifolds and (2) manifolds with small dual. (1) Morse-Bott degenerations: A Morse-Bott degeneration is a holomorphic map π : X → D from a Kähler manifold (X, Ω) to the unit disc D ⊂ C such that Crit(π) ⊂ π−1(0) and the holomorphic Hessian of π is a a non-degenerate quadratic form when restricted to the normal bundle of Crit(π) in X. Our first result on the subject is showing that Lagrangian submanifolds in the singularity locus of the degeneration L ⊂ Crit(π) ⊂ Σ0 give rise to Lagrangian submanifolds Nz(L) in Σz = π −1(z) in the smooth fibers z 6= 0. Moreover, Nz(L) ⊂ Σz is topologically a sphere bundle over L. This could be seen as a generalization of the well known result stating that fibers of a Lefschetz fibration admit Lagrangian spheres corresponding...
r i=1 O P s (a i)) be a Fano projective bundle over P s and denote by Crit(X) ⊂ (C *) n the solut... more r i=1 O P s (a i)) be a Fano projective bundle over P s and denote by Crit(X) ⊂ (C *) n the solution scheme of the Landau-Ginzburg system of equations of X. We describe a map E : Crit(X) → P ic(X) whose image E = {E(z)|z ∈ Crit(X)} is the full strongly exceptional collection described by Costa and Miró-Roig in [15]. We further show that Hom(E(z), E(w)) for z, w ∈ Crit(X) can be described in terms of a monodromy group acting on Crit(X).
For a toric Fano manifold X denote by Crit(X) ⊂ (C *) n the solution scheme of the Landau-Ginzbur... more For a toric Fano manifold X denote by Crit(X) ⊂ (C *) n the solution scheme of the Landau-Ginzburg system of equations of X. Examples of toric Fano manifolds with rk(P ic(X)) ≤ 3 which admit full strongly exceptional collections of line bundles were recently found by various authors. For these examples we construct a map E : Crit(X) → P ic(X) whose image E = {E(z)|z ∈ Crit(X)} is a full strongly exceptional collection satisfying the Maligned property. That is, under this map, the groups Hom(E(z), E(w)) for z, w ∈ Crit(X) are naturally related to the structure of the monodromy group acting on Crit(X).
In 1970, based on newly available empiric evidence, a remarkable monotonicity property for |ζ(z)|... more In 1970, based on newly available empiric evidence, a remarkable monotonicity property for |ζ(z)| was conjectured by R. Spira. The ζ-monotonicity property can be written as follows: |ζ(x 2 + yi)| < |ζ (x 1 + yi) | for any x 1 < x 2 ≤ 0.5 and 6.29 < y. In this work we present an experimental study of the monotonicity conjecture, in the course of which new properties of ζ(z) are discovered. For instance, the spectrum of semilimits λ(z) ⊂ R and the core function C(z), which serves as a non-chaotic simplification of ζ(z) to the left of the critical line
We show that the existence of a non-trivial solution of x n + y n = p n , with p a prime number, ... more We show that the existence of a non-trivial solution of x n + y n = p n , with p a prime number, is equivalent to the existence of a solution of a certain (over-determined) system of (n − 1)-recursion relations ("zipper" equations) in Z p−1 .
Let X be a toric Fano manifold and denote by Crit(f X) ⊂ (C *) n the solution scheme of the corre... more Let X be a toric Fano manifold and denote by Crit(f X) ⊂ (C *) n the solution scheme of the corresponding Landau-Ginzburg system of equations. For toric Del-Pezzo surfaces and various toric Fano threefolds we define a map L : Crit(f X) → P ic(X) such that E L (X) := L(Crit(f X)) ⊂ P ic(X) is a full strongly exceptional collection of line bundles. We observe the existence of a natural monodromy map M : π 1 (L(X) \ R X , f X) → Aut(Crit(f X)) where L(X) is the space of all Laurent polynomials whose Newton polytope is equal to the Newton polytope of f X , the Landau-Ginzburg potential of X, and R X ⊂ L(X) is the space of all elements whose corresponding solution scheme is reduced. We show that monodromies of Crit(f X) admit non-trivial relations to quiver representations of the exceptional collection E L (X). We refer to this property as the Maligned property of the maps L : Crit(f X) → P ic(X). We discuss possible applications of the existence of such Maligned exceptional maps to various aspects of mirror symmetry of toric Fano manifolds.
For X = P n the Euler sequence is given by 0 → Ω 1 P n → O n+1 P n (−1) → O P n → 0 We describe t... more For X = P n the Euler sequence is given by 0 → Ω 1 P n → O n+1 P n (−1) → O P n → 0 We describe the Lagrangian cobordism corresponding to this sequence via mirror symmetry, in the sense of Biran-Cornea. In particular, we describe the mirror Lagrangian of the cotangent sheaf Ω 1 P n ∈ D b (P n) in the mirror Fukaya category F uk(U ∆).
We study smooth projective varieties with small dual variety using methods from symplectic topolo... more We study smooth projective varieties with small dual variety using methods from symplectic topology. For such varieties we prove that the hyperplane class is an invertible element in the quantum cohomology of their hyperplane sections. We also prove that the affine part of such varieties are subcritical. We derive several topological and algebraic geometric consequences from that. The main tool in our work is the Seidel representation associated to Hamiltonian fibrations.
For $N \in \mathbb{N}$ consider the $N$-th section of the approximate functional equation $$ \zet... more For $N \in \mathbb{N}$ consider the $N$-th section of the approximate functional equation $$ \zeta_N(s)= \sum_{n =1 }^N B_n(s),$$ where $$ B_n(s)= \frac{1}{2} \left [ n^{-s} + \chi(s) \cdot n^{s-1} \right ].$$ Our aim in this work is to introduce a new approach for the Riemann hypothesis by studying the way pairs of consecutive zeros of $\zeta_N(s)$ change with respect to $N$. For the initial stage, it is known that the non-trivial zeros of $\zeta_1(s)$ all lie on the critical line $Re(s)=\frac{1}{2}$. In the region $2N \leq Im(s) \leq 2 \pi (N+1)$ the function $\zeta_N(s)$ serves as an approximation of $\zeta(s)$ itself, and it was conjectured by Spira that in this region $\zeta_N(s)$ also admits zeros only on the critical line. We show that the appearance of zeros of a section off the critical line can be realized as the result of two consecutive zeros meeting and pushing each other off the critical line as $N$ changes, a process to which we refer to as a collision of zeros. Based...
We show that the existence of a non-trivial solution of $x^n+y^n=p^n$, with $p$ a prime number, i... more We show that the existence of a non-trivial solution of $x^n+y^n=p^n$, with $p$ a prime number, is equivalent to the existence of a solution of a certain (over-determined) system of $(n-1)$-recursion relations ("zipper" equations) in $\mathbb{Z}_{p-1}$.
Our aim in this work is to present a modern study of the classical Riemann zeta function aided by... more Our aim in this work is to present a modern study of the classical Riemann zeta function aided by contemporary computational tools. One of our main discoveries in this work regarding $\zeta(z)$ is the observation of the following natural property (alongside various other new properties): $$ \vert \zeta (0.5 + y i ) \vert < \vert \zeta \left ( x+y i \right )\vert \hspace{0.5cm} \textrm {for all } \hspace{0.25cm} 0 \leq x<0.5 \textrm{ and } 6.29<y<Y,$$ with $0<<Y$ (we conjecture that $Y=+\infty$). In particular, the Riemann hypothesis is a direct consequence of the above property (in any domain which it holds) which gives a natural explanation to the fact that $\zeta(z)$ admits no zeros in the critical strip with $Re(z) \neq 0.5$.
Let X be a toric Fano manifold given by a reflexive polytope Δ and let Crit(f)⊂(C*)s be the solut... more Let X be a toric Fano manifold given by a reflexive polytope Δ and let Crit(f)⊂(C*)s be the solution scheme of the Landau–Ginzburg system associated with a Laurent polynomial fu(z)≔∑n∈Δ◦(0)∩Zsunzn∈L(Δ◦). Motivated by mirror symmetry, we construct a map E : Crit(fu) → Pic(X) and show various cases of (X, fu) for which its image Eu(X)≔E(z)|z∈Crit(fu)⊂Pic(X) is a full strongly exceptional collection of line bundles. Moreover, we study relations between Hom(E(z), E(w)) for z, w ∈ Crit(fu) and the structure of the monodromy group acting on Crit(fu). The construction relies on a study of the tropical and co-tropical properties of Crit(fu) as log|u| → ±∞.
Fermat, about 1637, stated that Itlt is impossible to separate a cube into two cubes, or a biquad... more Fermat, about 1637, stated that Itlt is impossible to separate a cube into two cubes, or a biquadrate into two biquadrates, or in general any power higher than the second into two powers of like degree; I have discovered a truly remarkable proof which (JJ this margin is too small to contain. 1t This theorem is known as Fermat's Last Theorem. This problem may be more simply stated by
Let X be a toric Del-Pezzo surface and let Crit(W) ⊂ (C *) n be the solution scheme of the Landau... more Let X be a toric Del-Pezzo surface and let Crit(W) ⊂ (C *) n be the solution scheme of the Landau-Ginzburg system of equations. Denote by X • the polar variety of X. Our aim in this work is to describe a map L : Crit(W) → F uk trop (X •) whose image under homological mirror symmetry corresponds to a full strongly exceptional collection of line bundles.
Let X be a toric Fano manifold and denote by Crit(f X) ⊂ (C *) n the solution scheme of the corre... more Let X be a toric Fano manifold and denote by Crit(f X) ⊂ (C *) n the solution scheme of the corresponding Landau-Ginzburg system of equations. For toric Del-Pezzo surfaces and various toric Fano threefolds we define a map L : Crit(f X) → P ic(X) such that E L (X) := L(Crit(f X)) ⊂ P ic(X) is a full strongly exceptional collection of line bundles. We observe the existence of a natural monodromy map M : π 1 (L(X) \ R X , f X) → Aut(Crit(f X)) where L(X) is the space of all Laurent polynomials whose Newton polytope is equal to the Newton polytope of f X , the Landau-Ginzburg potential of X, and R X ⊂ L(X) is the space of all elements whose corresponding solution scheme is reduced. We show that monodromies of Crit(f X) admit non-trivial relations to quiver representations of the exceptional collection E L (X). We refer to this property as the Maligned property of the maps L : Crit(f X) → P ic(X). We discuss possible applications of the existence of such Maligned exceptional maps to various aspects of mirror symmetry of toric Fano manifolds.
Proceedings of the American Mathematical Society, 2014
Morse-Bott fibrations generalize the class of Lefschetz fibrations, allowing for non-isolated sin... more Morse-Bott fibrations generalize the class of Lefschetz fibrations, allowing for non-isolated singularities. A Morse-Bott degeneration is a Morse-Bott fibration π : X → D whose only singular value is 0 ∈ D. We show that Morse-Bott degenerations with Crit(π) = CP k for 0 < k admit restrictions which are unique to the non-isolated case. These restrictions are obtained as an application of methods of Floer homology for monotone Lagrangian submanifolds.
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Papers by Yochay Jerby