diffstrata—A Sage Package for Calculations in the Tautological Ring of the Moduli Space of Abelian Differentials

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.

Keywords:

• Strata of abelian differentials
• intersection theory
• sage package

Declaration of Interest

No potential conflict of interest was reported by the author(s).

Notes

1 In practice, one runs out of memory before speed becomes a serious issue: Calculations in genus four take several hours but need several TB of RAM.

Additional information

Funding

Research of the second and third author is supported by the DFG-project MO 1884/2-1 and by the LOEWE-Schwerpunkt “Uniformisierte Strukturen in Arithmetik und Geometrie.”