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2014 Local cohomology with support in generic determinantal ideals
Claudiu Raicu, Jerzy Weyman
Algebra Number Theory 8(5): 1231-1257 (2014). DOI: 10.2140/ant.2014.8.1231

Abstract

For positive integers mnp, we compute the GLm×GLn-equivariant description of the local cohomology modules of the polynomial ring S= Sym(mn) with support in the ideal of p×p minors of the generic m×n matrix. Our techniques allow us to explicitly compute all the modules ExtS(SIx¯,S), for x¯ a partition and Ix¯ the ideal generated by the irreducible subrepresentation of S indexed by x¯. In particular we determine the regularity of the ideals Ix¯, 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. "Local cohomology with support in generic determinantal ideals." Algebra Number Theory 8 (5) 1231 - 1257, 2014. https://doi.org/10.2140/ant.2014.8.1231

Information

Received: 27 September 2013; Revised: 25 February 2014; Accepted: 26 March 2014; Published: 2014
First available in Project Euclid: 20 December 2017

zbMATH: 1303.13018
MathSciNet: MR3263142
Digital Object Identifier: 10.2140/ant.2014.8.1231

Subjects:
Primary: 13D45
Secondary: 14M12

Rights: Copyright © 2014 Mathematical Sciences Publishers

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