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arXiv · 1309.0617

Local cohomology with support in generic determinantal ideals

Claudiu Raicu·Jerzy Weyman
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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.

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Claudiu Raicu, Jerzy Weyman. 2013-09-03. Local cohomology with support in generic determinantal ideals. https://doi.org/10.2140/ant.2014.8.1231

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