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arXiv · 1305.1719

Local cohomology with support in ideals of maximal minors and sub-maximal Pfaffians

Claudiu Raicu·Jerzy Weyman·Emily E. Witt
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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.

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Claudiu Raicu, Jerzy Weyman, Emily E. Witt. 2013-10-09. Local cohomology with support in ideals of maximal minors and sub-maximal Pfaffians. https://doi.org/10.1016/j.aim.2013.10.005

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