Abstract

The tautological ring of the moduli space of stable curves has been studied extensively in the last decades. We present a SageMath implementation of many core features of this ring. This includes lists of generators and their products, intersection numbers and verification of tautological relations. Maps between tautological rings induced by functoriality, that is pushforwards and pullbacks under gluing and forgetful maps, are implemented. Furthermore, many interesting cycle classes, such as the double ramification cycles, strata of $k$-differentials and hyperelliptic or bielliptic cycles are available. We show how to apply the package, including concrete example computations.

Keywords

Mathematical Subject Classification 2010

Supplementary material

Sage module to compute with the tautological ring of the moduli space of complex curves

Milestones

Authors