Faber's socle intersection numbers via Gromov--Witten theory of elliptic curve

Abstract

The goal of this very short note is to give a new proof of Faber's formula for the socle intersection numbers in the tautological ring of ${\mathcal{M}}_g$. This new proof exhibits a new beautiful tautological relation that stems from the recent work of Oberdieck--Pixton on the Gromov--Witten theory of the elliptic curve via a refinement of their argument, and some straightforward computation with the double ramification cycles that enters the recursion relations for the Hamiltonians of the KdV hierarchy.

References in corpus (9)

• Virasoro constraints and the Chern classes of the Hodge bundle
• Double ramification cycles and integrable hierarchies
• Integrals of psi-classes over double ramification cycles
• Holomorphic anomaly equations and the Igusa cusp form conjecture
• A new proof of Faber's intersection number conjecture
• Tautological relations and integrable systems
• Half-Spin Tautological Relations and Faber's Proportionalities of Kappa Classes
• Combinatorics of binomial decompositions of the simplest Hodge integrals
• Recursion relations for Double Ramification Hierarchies