Let π : X → C be a relatively minimal non-isotrivial elliptic surface over the field of complex n... more Let π : X → C be a relatively minimal non-isotrivial elliptic surface over the field of complex numbers, where g(C) ≥ 2. In this article, we demonstrate an equivalence between the category of semistable parabolic Higgs bundles on C, and the category of semistable Higgs bundles on X with vanishing second Chern class, and determinant a vertical divisor. Contents 1. Introduction 1 Motivation and statement of results 1 Strategy 2 Related work and further comments 3 Acknowledgement 3 2. Preliminaries 3 2.1. Elliptic surfaces 4 2.2. Vertical Bundles 5 3. Main Theorem 8 3.1. Proof of Theorem 1 in the case of no multiple fibers 9 3.2. Proof of Theorem 1 in the case of multiple fibers 13 References 15
Let π : X → C be a relatively minimal non-isotrivial elliptic surface over the field of complex n... more Let π : X → C be a relatively minimal non-isotrivial elliptic surface over the field of complex numbers, where g(C) ≥ 2. In this article, we demonstrate an equivalence between the category of semistable parabolic Higgs bundles on C, and the category of semistable Higgs bundles on X with vanishing second Chern class, and determinant a vertical divisor. Contents 1. Introduction 1 Motivation and statement of results 1 Strategy 2 Related work and further comments 3 Acknowledgement 3 2. Preliminaries 3 2.1. Elliptic surfaces 4 2.2. Vertical Bundles 5 3. Main Theorem 8 3.1. Proof of Theorem 1 in the case of no multiple fibers 9 3.2. Proof of Theorem 1 in the case of multiple fibers 13 References 15
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