通过椭圆曲线的Gromov-Witten理论得到Faber的交点数

IF 0.9 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2025-06-23 DOI:10.1112/blms.70117

Xavier Blot, Sergey Shadrin, Ishan Jaztar Singh

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引用次数: 0

摘要

这篇短文的目的是给出M $\mathcal {M}_g$的同义环上的交点数的Faber公式的一个新的证明。这个新的证明展示了一个新的美丽的重言式关系，它源于Oberdieck-Pixton最近对椭圆曲线的Gromov-Witten理论的研究，通过对他们的论证的改进，以及一些直接的计算，这些计算进入了KdV层次的哈密顿量的递推关系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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

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

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 $M_{g}$ . 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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