Connecting Hodge integrals to GromovWitten invariants by Virasoro operators
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 GromovWitten 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 KontsevichWitten taufunction 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.
 Publication:

arXiv eprints
 Pub Date:
 December 2017
 DOI:
 10.48550/arXiv.1712.02331
 arXiv:
 arXiv:1712.02331
 Bibcode:
 2017arXiv171202331L
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematical Physics;
 Mathematics  Differential Geometry
 EPrint:
 21 pages