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arXiv · 1712.02331

Connecting Hodge integrals to Gromov-Witten invariants by Virasoro operators

Xiaobo Liu·Haijiang Yu
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Abstract

In this paper, we show that the generating function for linear Hodge integrals over moduli spaces of stable maps to a nonsingular projective variety $X$ can be connected to the generating function for Gromov-Witten invariants of $X$ by a series of differential operators $\{ L_m \mid m \geq 1 \}$ after a suitable change of variables. These operators satisfy the Virasoro bracket relation and can be seen as a generalization of the Virasoro operators appeared in the Virasoro constraints for Kontsevich-Witten tau-function in the point case. This result is an extension of the work in \cite{LW} for the point case which solved a conjecture of Alexandrov.

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Xiaobo Liu, Haijiang Yu. 2017-12-06. Connecting Hodge integrals to Gromov-Witten invariants by Virasoro operators. https://arxiv.org/abs/1712.02331

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