|Date: Wednesday, November 15, 2017
Location: 4096 East Hall (4:10 PM to 5:30 PM)
Title: GIT for syzygies, with applications
Abstract: I will introduce geometric invariant theory (GIT) of syzygy points of polarized varieties. A syzygy point is a natural Koszul-theoretic generalization of a Hilbert point, and encodes higher-order relations among generators of the homogeneous ideal of an embedded variety. While GIT for Hilbert points has been classically used to construct moduli spaces of polarized varieties by Mumford, Gieseker, Viehweg, and many others, the GIT of syzygy points is much less explored. In this talk, I will present two cases where the GIT stability analysis of syzygy points is feasible: canonical curves, and polarized K3 surfaces. Applications will include a new construction in the Hassett-Keel program for the moduli space of genus 6 curves and an effectivity result for divisors on the moduli space of K3 surfaces of odd genus.
Speaker: Maksym Fedorchuk
Institution: Boston College