DMS Algebra Seminar

Speaker: Xianglong Ni (UC-Berkeley)

Title: Schubert varieties and the structure of codimension three perfect ideals

Abstract: In the orthogonal Grassmannian OG\((n,2n)\), there are two (opposite) Schubert varieties of codimension three. Their restrictions to the big affine open cell are cut out by equations familiar to commutative algebraists. For example, one is defined by the submaximal Pfaffians of a generic skew matrix---thus, by the structure theorem of Buchsbaum and Eisenbud, it is the universal example of a Gorenstein ideal of codimension three on \(n\) generators. The other gives the universal example of an almost complete intersection of type \(n-3\). I will explain how this example relates to Weyman's work on generic free resolutions of length three, and how it conjecturally extends to perfect ideals with other particular Betti numbers.