The stable hyperelliptic locus in genus 3: An application of Porteous Formula

Abstract

We compute the class of the closure of the locus of hyperelliptic curves in the moduli space of stable genus-3 curves in terms of the tautological class $\lambda$ and the boundary classes ${\delta }_0$ and ${\delta }_1$. The expression of this class is known, but here we compute it directly, by means of Porteous Formula, without resorting to blowups or test curves.