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

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

References in corpus (2)

• Masur-Veech volumes and intersection theory: the principal strata of quadratic differentials
• Boundary Expression for Chern Classes of the Hodge Bundle on Spaces of Cyclic Covers

Cited by in corpus (17)

• The Virasoro Minimal String
• Double Hurwitz numbers: polynomiality, topological recursion and intersection theory
• Masur-Veech volumes and intersection theory: the principal strata of quadratic differentials
• The Chow rings of the moduli spaces of curves of genus 7, 8, and 9
• Pixton's formula and Abel-Jacobi theory on the Picard stack
• Volumes of moduli spaces of flat surfaces
• diffstrata -- a Sage package for calculations in the tautological ring of the moduli space of Abelian differentials
• On the Goulden-Jackson-Vakil conjecture for double Hurwitz numbers
• A conjectural formula for $D{R}_g(a,-a){\lambda }_g$
• Extensions of tautological rings and motivic structures in the cohomology of ${\overline{\mathcal{M}}}_{g,n}$
• Stable tree expressions with Omega-classes and Double Ramification cycles
• Completed Cycles Leaky Hurwitz Numbers
• On some hyperelliptic Hurwitz-Hodge integrals
• d-elliptic loci in genus 2 and 3
• Quadratic Pseudostable Hodge Integrals and Mumford's Relations
• The tautological ring of ${\overline{\mathcal{M}}}_{g,n}$ is rarely Gorenstein
• The birational geometry of moduli of cubic surfaces and cubic surfaces with a line