Alexandra Seceleanu

ABSTRACT

A $m \times n$ matrix with indeterminate entries admits a natural action of the group $\text{GL}_m \times \text{GL}_n$ by changes of bases. In a landmark 1980 paper, DeConcini, Eisenbud, and Procesi studied determinantal ideals, which are invariant under this group action, describing their primary decomposition, integral closures, and symbolic powers. In particular, interest in symbolic powers is motivated by the fact that they encode functions vanishing to high order on certain symmetric varieties. In this talk we study related families of GL-invariant ideals with the goal of combinatorially describing their symbolic powers in in the spirit of Schubert calculus and computing asymptotic invariants which measure their growth.

This is joint work with Sankhaneel Bisui.