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

By Vincent Delecroix, Johannes Schmitt, J. V. Zelm. The Journal of Software for Algebra and Geometry, 2020

54 citations recorded by the source corpus.

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. In this paper we show how to apply the package, including concrete example computations.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0872290ab5b8431ce3bf5f47d7b9fb099144aea3

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In Computational Theory and Mathematics

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Citations in the corpus

• The Chern classes and Euler characteristic of the moduli spaces of Abelian differentials (2020, methodology): “The evaluation of these formulas is performed by a sage package diffstrata that builds on the package admcycles for computation in the moduli space of curves ([DSZ20]).”