A class of perfect determinantal ideals

Journal of Algebra, 2001

Contemporary Mathematics, 1994

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Manuscripta Mathematica, 1981

2014

We study higher jumping numbers and generalized test ideals associated to determinantal ideals over a field of positive characteristic. We work in positive characteristic to give a complete characterization of both families for ideals generated by maximal minors; and make a conjecture for the general case. Although these invariants are understood asymptotically, as their positive characteristic grows to infinity they essentially coincide with their characteristic zero analogues, there are known examples where the behavior in positive characteristic differs significantly from that of characteristic zero. This new knowledge associated to determinantal ideals strengthens the case that test ideals and multiplier ideals exhibit essentially the same description.

Partially supported by NSF grant DMS-8301870. 159 160 J. HERZOG, W. V. VASCONCELOS AND R. VILLARREAL stein precisely when I is strongly Cohen-Macaulay ([9, (6.5)]).

Advances in Mathematics, 1981

Journal of Algebra, 1983

Proceedings of the American Mathematical Society, 1999

Abstract. We give a combinatorial proof of the Dedekind–Mertens formula by computing the initial ideal of the content ideal of the product of two generic polynomials. As a side effect we obtain a complete classification of the rank 1 Cohen–Macaulay modules over the determinantal ...

American Journal of Mathematics, 2004

We prove new height inequalities for determinantal ideals in a regular local ring, or more generally in a local ring of given embedding codimension. Our theorems extend and sharpen results of Faltings and Bruns.

Archiv der Mathematik, 1989