Local cohomology with support in generic determinantal ideals

Abstract

For positive integers m >= n >= p, we compute the GL_m x GL_n-equivariant description of the local cohomology modules of the polynomial ring S of functions on the space of m x n matrices, with support in the ideal of p x p minors. Our techniques allow us to explicitly compute all the modules Ext_S(S/I_x,S), for x a partition and I_x the ideal generated by the irreducible sub-representation of S indexed by x. In particular we determine the regularity of the ideals I_x, and we deduce that the only ones admitting a linear free resolution are the powers of the ideal of maximal minors of the generic matrix, as well as the products between such powers and the maximal ideal of S.

References in corpus (1)

• Local cohomology with support in ideals of maximal minors and sub-maximal Pfaffians

Cited by in corpus (15)

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• Regularity of S_n-invariant monomial ideals
• A note on the multiplicities of the determinantal thickenings of maximal minors
• Lengths of Local Cohomology of Thickenings
• Local cohomology -- an invitation