UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

September 11, 2018

939 Evans Hall

3:45PM: The geometry of moduli spaces of curves

Frank-Olaf Schreyer

In this expository talk, we discuss from an elementary point of view how one approaches studying the geometry of moduli spaces of curves. We begin with classical examples of how one can prove that some moduli spaces are unirational. At the opposite extreme, following ideas of Harris, Mumford, Eisenbud and Farkas, we then explain how one can reduce proving that moduli spaces are of general type to the study of carefully chosen effective divisors on them.

5:00PM: The strong maximal rank conjecture and moduli spaces of curves

Brian Osserman

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.

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