Algebra & Number Theory

Local cohomology with support in generic determinantal ideals

Claudiu Raicu and Jerzy Weyman

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

local cohomology determinantal ideals regularity


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.

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