Connecting Hodge integrals to Gromov-Witten invariants by Virasoro operators
- Resource Type
- Working Paper
- Authors
- Liu, Xiaobo; Yu, Haijiang
- Source
- Subject
- Mathematics - Algebraic Geometry
Mathematical Physics
Mathematics - Differential Geometry
- Language
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.
Comment: 21 pages