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 (15)

• Double ramification cycles on the moduli spaces of curves
• Compactification of strata of abelian differentials
• The moduli space of twisted canonical divisors
• Constructions of nontautological classes on moduli spaces of curves
• Relations on ${\overline{M}}_{g,n}$ via equivariant Gromov-Witten theory of ${\mathbb{P}}^1$
• Pixton's double ramification cycle relations
• The stability space of compactified universal Jacobians
• Extending the Double Ramification Cycle using Jacobians
• Masur-Veech volumes and intersection theory: the principal strata of quadratic differentials
• The hypergeometric functions of the Faber-Zagier and Pixton relations
• Quadratic double ramification integrals and the noncommutative KdV hierarchy
• Infinitesimal structure of the pluricanonical double ramification locus
• Calculating intersection numbers on moduli spaces of pointed curves
• Boundary Expression for Chern Classes of the Hodge Bundle on Spaces of Cyclic Covers
• Pullbacks of universal Brill-Noether classes via Abel-Jacobi morphisms

Cited by in corpus (20)

• The Virasoro Minimal String
• A new cohomology class on the moduli space of curves
• Double Hurwitz numbers: polynomiality, topological recursion and intersection theory
• Masur-Veech volumes and intersection theory: the principal strata of quadratic differentials
• Quadratic double ramification integrals and the noncommutative KdV hierarchy
• 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
• A Laplacian to compute intersection numbers on ${\bar{\mathcal{M}}}_{g,n}$ and correlation functions in NCQFT
• 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 ${\overline{\mathcal{M}}}_{g,n}$
• Completed Cycles Leaky Hurwitz Numbers
• On some hyperelliptic Hurwitz-Hodge integrals
• Stable tree expressions with Omega-classes and Double Ramification cycles
• 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