Connecting Hodge integrals to Gromov-Witten invariants by Virasoro operators

2017/12/06 by Liu, Xiaobo, Yu, Haijiang
#Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1712.02331

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 | m ≥ 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 \citeLW for the point case which solved a conjecture of Alexandrov.

Related

• Virasoro constraints for Hodge integrals
• Hodge integrals and Gromov-Witten theory
• The Virasoro conjecture for Gromov-Witten invariants
• Virasoro constraints for stable pairs on toric 3-folds
• Hodge integrals and λ_g conjecture with target varieties