Local cohomology with support in ideals of maximal minors and sub-maximal Pfaffians
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 Gm. 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.
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.