Algebraic Geometry Seminar: "Virtual Resolutions of Monomial Ideals"

Abstract: Virtual Resolutions as introduced by Berkesch, Erman, and Smith give an alternative to minimal free resolutions for studying syzygies in the multigraded setting. In particular, for subvarieties of a smooth normal toric varieties, these virtual resolutions provide a way of considering syzygies that better reflects the geometry of the subvariety. I will discuss recent work, including joint work with Berkesch, Klein, and Loper, where we have explored the case of monomial ideals. In particular, I discuss bounds on the lengths of these virtual resolutions, and the virtually Cohen--Macaulay property.

Host: Matt Kerr