Effective divisors in $\overline{\mathcal{M}}_{g,n}$ from abelian differentials

TL;DR

This paper introduces a new method to compute effective divisors in the moduli space of curves using abelian differentials, reproducing known results and discovering new classes.

Contribution

It develops a novel approach leveraging maps between moduli spaces and abelian differential degenerations to compute effective divisors.

Findings

Computed many new classes of effective divisors in ar{al M}_{g,n}

Reproduced numerous known results using the new method

Enhanced understanding of the structure of the moduli space via abelian differentials

Abstract

We compute many new classes of effective divisors in $\overline{\mathcal{M}}_{g,n}$ coming from the strata of abelian differentials and efficiently reproduce many known results obtained by alternate methods. Our method utilises maps between moduli spaces and the degeneration of abelian differentials.