Angelina Zheng: Stable cohomology of the moduli space of trigonal curves

Abstract

We study the rational cohomology of the moduli space of trigonal curves of fixed genus. Specifically, we prove that, similarly to the cohomology of the moduli space of smooth curves, the cohomology ring stabilizes and it coincides with the tautological ring within the stable range. This will be done by studying the natural embedding of trigonal curves in Hirzebruch surfaces and by using Gorinov-Vassiliev's method for the cohomology of complements of discriminants.