Combinatorics Seminar

Geometric vertex decomposition and liaison are two frameworks that have been used to produce similar results about similar families of algebraic varieties. In this talk, we will describe an explicit connection between these approaches. In particular, we describe how each geometrically vertex decomposable ideal is linked by a sequence of elementary G-biliaisons of height 1 to an ideal of indeterminates and, conversely, how every G-biliaison of a certain type gives rise to a geometric vertex decomposition. This connection gives us a framework for implementing with relative ease Gorla, Migliore, and Nagel's strategy of using liaison to establish Gröbner bases. We describe an approach to understanding diagonal degenerations of matrix Schubert varieties along these lines.

This talk is based on joint work with Jenna Rajchgot and with Anna Weigandt.
Speaker(s): Patricia Klein (University of Minnesota)