Department of

Mathematics

Seminar Calendar
for events the day of Thursday, September 17, 2020.

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Thursday, September 17, 2020

3:00 pm in Zoom,Thursday, September 17, 2020

Geometric vertex decomposition and liaison

Patricia Klein   [email] (University of Minnesota)

Abstract: 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. As a consequence, we can immediately conclude that several well-known families of ideals are glicci, including Schubert determinantal ideals, defining ideals of varieties of complexes, and defining ideals of graded lower bound cluster algebras. This connection also gives us a framework for implementing with relative ease Gorla, Migliore, and Nagel’s strategy of using liaison to establish Gröbner bases. We describe briefly, as an application of this work, a proof of a recent conjecture of Hamaker, Pechenik, and Weigandt on diagonal Gröbner bases of Schubert determinantal ideals. This talk is based on joint work with Jenna Rajchgot. Please email Colleen at cer2 (at) illinois (dot) edu for the Zoom ID and password.

5:30 pm in Zoom Meeting,Thursday, September 17, 2020