Translator Disclaimer
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


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.


Download Citation

Claudiu Raicu. Jerzy Weyman. "Local cohomology with support in generic determinantal ideals." Algebra Number Theory 8 (5) 1231 - 1257, 2014.


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

Primary: 13D45
Secondary: 14M12

Rights: Copyright © 2014 Mathematical Sciences Publishers


Vol.8 • No. 5 • 2014
Back to Top