Local cohomology with support in ideals of maximal minors and sub-maximal Pfaffians
arXiv:1305.1719 · doi:10.1016/j.aim.2013.10.005
Abstract
We compute the GL-equivariant description of the local cohomology modules with support in the ideal of maximal minors of a generic matrix, as well as of those with support in the ideal of 2n x 2n Pfaffians of a (2n+1)x(2n+1) generic skew-symmetric matrix. As an application, we characterize the Cohen-Macaulay modules of covariants for the action of the special linear group SL(G) on G^m. The main tool we develop is a method for computing certain Ext modules based on the geometric technique for computing syzygies and on Matlis duality.
v2: minor changes, references added, to appear in Advances in Mathematics
References in corpus (1)
Cited by in corpus (9)
- Local cohomology with support in generic determinantal ideals
- Characters of equivariant D-modules on spaces of matrices
- Local cohomology with support in ideals of symmetric minors and Pfaffians
- Equivariant D-modules on alternating senary 3-tensors
- Homological invariants of determinantal thickenings
- Equivariant D-modules on 2x2x2 hypermatrices
- Vanishing cotangent cohomology for Plücker algebras
- Characters of equivariant D-modules on Veronese cones
- Lengths of Local Cohomology of Thickenings