Seminar

I will report on joint work with Claudiu Raicu and Emily Witt on computing the GL-equivariant description of the local cohomology modules with support in the ideal of maximal minors of a generic matrix. I will explain the main tools that we employ in our study, namely (1) the BGG correspondence between the homology groups of linear complexes over a polynomial ring and minimal free resolutions over the exterior algebra, and (2) the exterior algebra analogue of the geometric technique for computing syzygies. If time permits, I will mention how the same techniques apply to give the description of the local cohomology modules with support in the ideal of 2n x 2n Pfaffians of a (2n+1) x (2n+1) generic skew-symmetric matrix, and mention a possible approach to extend our results to the case of non-maximal minors.