Algebra & Number Theory

Local cohomology with support in generic determinantal ideals

Claudiu Raicu and Jerzy Weyman

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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.

Article information

Source
Algebra Number Theory, Volume 8, Number 5 (2014), 1231-1257.

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

Permanent link to this document
https://projecteuclid.org/euclid.ant/1513730230

Digital Object Identifier
doi:10.2140/ant.2014.8.1231

Mathematical Reviews number (MathSciNet)
MR3263142

Zentralblatt MATH identifier
1303.13018

Subjects
Primary: 13D45: Local cohomology [See also 14B15]
Secondary: 14M12: Determinantal varieties [See also 13C40]

Keywords
local cohomology determinantal ideals regularity

Citation

Raicu, Claudiu; Weyman, Jerzy. Local cohomology with support in generic determinantal ideals. Algebra Number Theory 8 (2014), no. 5, 1231--1257. doi:10.2140/ant.2014.8.1231. https://projecteuclid.org/euclid.ant/1513730230


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