Divisorial strata of abelian differentials

TL;DR

This paper provides a closed formula for the class of the closure of the locus of algebraic curves with abelian differentials of a specified signature, advancing the understanding of the geometry of moduli spaces.

Contribution

It introduces a new explicit formula for the class of divisorial strata of abelian differentials in the moduli space of curves.

Findings

Derived a closed-form expression for the class of the divisor

Applied the formula to specific signatures to compute classes

Enhanced understanding of the geometry of abelian differentials

Abstract

We compute a closed formula for the class of the closure of the locus of curves in $\overline{\mathcal{M}}_g$ that admit an abelian differential of signature $\kappa=(k_1,...,k_{g-2})$.