Algebraic Geometry Seminar
Claudiu Raicu
Princeton University
Local cohomology with support in generic determinantal ideals
Abstract: The space $Mat(m,n)$ of $m\times n$ matrices admits a natural action of the group $\textrm{GL}_m \times \textrm{GL}_n$ via row and column operations on the matrix entries. The invariant closed subsets are the closures of the orbits of constant rank matrices. I will explain how to describe the local cohomology modules of the ring $S$ of polynomial functions on $Mat(m,n)$ with support in these orbit closures, and mention some consequences of the methods employed to computing minimal free resolutions of invariant ideals in $S$. These ideals correspond to nilpotent scheme structures on the orbit closures, and their study goes back to the work of De Concini, Eisenbud and Procesi in the 80s. Joint work with Jerzy Weyman.
Wednesday October 30, 2013 at 4:00 PM in SEO 427