diffstrata -- a Sage package for calculations in the tautological ring of the moduli space of Abelian differentials

TL;DR

The paper introduces the diffstrata Sage package, which provides algorithms for enumerating boundary components and performing intersection theory on the compactification of strata of abelian differentials, facilitating complex calculations.

Contribution

It presents new algorithms implemented in SageMath for boundary enumeration and intersection theory in the moduli space of abelian differentials.

Findings

Efficient enumeration of boundary components

Calculation of Euler characteristics of strata

Implementation of intersection theory algorithms

Abstract

The boundary of the multi-scale differential compactification of strata of abelian differentials admits an explicit combinatorial description. However, even for low-dimensional strata, the complexity of the boundary requires use of a computer. We give a description of the algorithms implemented in the SageMath package diffstrata to enumerate the boundary components and perform intersection theory on this space. In particular, the package can compute the Euler characteristic of strata using the methods developed by the same authors in [CMZ20].