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arXiv · 2502.02297

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

Xavier Blot·Sergey Shadrin·Ishan Jaztar Singh
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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.

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Xavier Blot, Sergey Shadrin, Ishan Jaztar Singh. 2025-02-04. Faber's socle intersection numbers via Gromov--Witten theory of elliptic curve. https://doi.org/10.1112/blms.70117

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