Vol. 11, No. 1, 2021

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admcycles - a Sage package for calculations in the tautological ring of the moduli space of stable curves

Vincent Delecroix, Johannes Schmitt and Jason van Zelm

Vol. 11 (2021), 89–112
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
moduli of curves, tautological ring, intersection theory, double ramification cycle
Mathematical Subject Classification 2010
Primary: 14H10, 97N80
Supplementary material

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

Milestones
Received: 16 March 2020
Revised: 30 June 2021
Accepted: 15 July 2021
Published: 20 February 2022
Authors
Vincent Delecroix
Laboratoire Bordelais de Recherche en Informatique
CNRS - Université de Bordeaux
Talence
France
Johannes Schmitt
Mathematical Institute
University of Bonn
Bonn
Germany
Jason van Zelm
Humboldt Universität zu Berlin
Berlin
Germany