Algebra And Algebraic Geometry Seminar - Jay Yang - Virtually Cohen--Macaulay Monomial Ideals


Speaker: Jay Yang (McMaster University)

Title: Virtually Cohen--Macaulay Monomial Ideals

Abstract: Virtual resolutions are a recent idea developed first by Berkesch, Erman, and Smith to provide a new approach to studying syzygies of modules over the Cox ring of a toric variety. I discuss a joint paper with Berkesch, Klien, and Loper in which we consider virtually Cohen--Macaulay ideals. Our results are primarily for monomial ideals, where we use the tools of Stanley-Reisner theory to prove that certain squarefree monomial ideals are virtually Cohen--Macaulay. We also consider a definition of virtually regular element, and a basic result on how it interacts with the virtually Cohen--Macaulay property. Much remains unknown about virtually Cohen--Macaulay ideals, even in the monomial case.

Location: Virtual

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