# Algebra Seminar

Date:

10/23/2019 - 2:00pm to 3:00pm

Location:

745 POT

Speaker(s) / Presenter(s):

Michael Loper, University of Minnesota

Title: What Makes a Complex Virtual

Abstract: Let $S$ be the Cox ring of a smooth toric variety and $B$ be the irrelevant ideal. In 2017, Berkesch, Erman, and Smith introduced virtual resolutions for toric varieties as an analogue of minimal free resolutions for projective varieties. Virtual resolutions are complexes of free $S$-modules that allow $B$-torsion homology. I will discuss virtual resolutions and name two algebraic conditions that determine whether a bounded chain complex of free $S$-modules is a virtual resolution. This theorem is similar to the depth criterion of exactness that Buchsbaum and Eisenbud published in 1973.

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