Nicola Tarasca : Loci of curves with subcanonical points in low genus

Posted by Kevin Tucker , part of the Algebraic Geometry Seminar.

At

Oct. 14, 2015, 4 p.m.

In

SEO 427

Abstract

In this talk, I will discuss loci of curves with subcanonical points inside moduli spaces of curves. For instance, the locus of curves of genus 3 with a marked subcanonical point has two components: the locus of hyperelliptic curves with a marked Weierstrass point, and the locus of non-hyperelliptic curves with a marked hyperflex. I will show how to compute the classes of the closures of these codimension-two loci in the moduli space of stable curves of genus 3 with a marked point. Similarly, I will present the class of the closure of the locus of curves of genus four with an even theta characteristic vanishing with order three at a certain point. Finally, I will discuss the geometric consequences of these computations. This is joint work with Dawei Chen.