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### arXiv:1712.02331 [math.AG]AbstractReferencesReviewsResources

#### Connecting Hodge integrals to Gromov-Witten invariants by Virasoro operators

Published 2017-12-06Version 1

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.

On Gromov--Witten invariants of $\mathbb{P}^1$