Changho Han, Department of Pure Mathematics, University of Waterloo
"Aspects of genus 4 curves"
If you know several different ways to characterize a given projective variety, then you can gain knowledge of the properties of this object by interconnecting methods involved in different viewpoints. For example, one can interconnect both algebraic and analytic methods to study complex elliptic curves, which could be viewed as either plane cubic curves or lattice quotients of a complex plane. Motivated by this principle, we will explore various different ways to characterize a general genus 4 curve, and then see how those viewpoints can be extended to special genus 4 curves as well. In particular, I will show that general genus 4 curves can alternatively be characterized by trigonal maps to projective line, bidegree (3,3)-curves in a smooth quadric surface, or particular kinds of K3 surfaces. If time remains, then I will explain how those viewpoints induce birational maps between corresponding moduli spaces. This talk is based on a pictorial portion of joint works in progress with Valery Alexeev, Anand Deopurkar, and Philip Engel.
MC 5417