Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring: The strong maximal rank conjecture and moduli spaces of curves
Seminar | September 11 | 5-6 p.m. | 939 Evans Hall
Brian Osserman, UC Davis
Following work of Farkas, in order to prove that the moduli spaces of curves of genus 22 (respectively, 23) are of general type, it suffices to prove that not every curve in them admits a morphism to projective 6-space of degree 25 (respectively, 26) whose image lies on a quadric. We describe a proof of this statement via a degeneration argument, combining ideas from the Eisenbud-Harris theory of limit linear series and the more recent theory of linked linear series. This is joint work with Fu Liu, Montserrat Teixidor i Bigas, and Naizhen Zhang.