Keller VandeBogert
University of Kentucky
Title
Syzygies and Stability for Grassmannian Matrix Schubert Varieties
Abstract
Matrix Schubert varieties naturally generalize determinantal varieties by allowing one to impose rank conditions on specified submatrices. Knutson–Miller identify their equivariant K-polynomials, which record alternating sums of syzygy characters, with double Grothendieck polynomials. A recent conjecture of Price–Stelzer–Yong predicts stability in the Schur supports of these polynomials as the underlying permutations are enlarged. In this talk, I’ll discuss a stronger phenomenon for Grassmannian matrix Schubert varieties: the individual syzygy representations stabilize, with multiplicities and homological degrees unchanged, under a simple operation on Young diagrams called Durfee stabilization. I’ll explain how the geometry of their desingularizations allows us to prove this through vector bundle cohomology on flag varieties and determine the sharp stability range. This is based on joint work with Sasha Pevzner, Steven V Sam, and Linus Setiabrata.
