Conjectural relations in the tautological ring of ${\bar{M}}_{g,n}$

Abstract

We describe a very large class of conjectural relations in the tautological ring of the moduli space ${\bar{M}}_{g,n}$ of stable curves of genus $g$ with $n$ marked points, extending and generalizing the Faber-Zagier relations. These notes are loosely based on informal talks given by the author at the workshop at KTH Stockholm on "The moduli space of curves and its intersection theory" in April 2012.

arXiv comment7 pages

References in corpus (2)

• Relations in the tautological ring
• Calculating intersection numbers on moduli spaces of pointed curves

Cited by in corpus (15)

• Relations in the tautological ring of the moduli space of curves
• Relations on ${\overline{M}}_{g,n}$ via equivariant Gromov-Witten theory of ${\mathbb{P}}^1$
• The partition function of the extended $r$-reduced Kadomtsev-Petviashvili hierarchy
• Relations on Mbar_{g,n} via 3-spin structures
• Tautological relations in moduli spaces of weighted pointed curves
• Ramanujan Identities and Quasi-Modularity in Gromov-Witten Theory
• Tautological relations via r-spin structures
• The Chern character of the Verlinde bundle over the moduli space of stable curves
• Comparing tautological relations from the equivariant Gromov-Witten theory of projective spaces and spin structures
• Topological recursion relations from Pixton's formula
• A conjectural connection between R^*(C_g^n) and R^*(M_{g,n}^rt)
• The moduli space of curves and its invariants
• Relations on Mbar_{g,n} via orbifold stable maps
• A genus-4 topological recursion relation for Gromov-Witten invariants
• Relations in the Tautological Ring of the Universal Curve