We derive some quadratic recursion relations for some Hodge integrals by virtual localization and obtain many closed formulas. We apply our formulas to the local geometry of toric Fano surfaces in a Calabi-Yau threefo...We derive some quadratic recursion relations for some Hodge integrals by virtual localization and obtain many closed formulas. We apply our formulas to the local geometry of toric Fano surfaces in a Calabi-Yau threefold and compute some of the numbers $n_\beta ^g$ in Gopakumar-Vafa's formula for all g in this case.展开更多
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 invar...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 differen-tial 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 a generalization of the work in Liu and Wang[Commun.Math.Phys.346(1):143-190,2016]for the point case which solved a conjecture of Alexandrov.展开更多
Hodge integrals over moduli space of stable curves play an important roles in understanding the topological properties of moduli space. ELSV formula connects the Hodge integrals with Hurwitz numbers, and the generatin...Hodge integrals over moduli space of stable curves play an important roles in understanding the topological properties of moduli space. ELSV formula connects the Hodge integrals with Hurwitz numbers, and the generating function of Hurwitz numbers satisfies the cut-and-join equation. Therefore, it is natural to consider how to use the cut-and-join equation for Hurwitz numbers to compute Hodge integrals which appear in ELSV formula. In this paper, at first, we will review the method introduced in Goulden et al.＇s paper to get the λg conjecture for Hodge integral. Through some variables transformation, the generating function of Hurwitz number becomes a symmetric polynomial which satisfies a symmetrized cut-and-join equation. By comparing the coefficients of the lowest degree term of both sides in this equation, we can get the ,λg conjecture. Then, in a similar way, we obtain our main result in this paper： a recursive formula for Hodge integral of type contains only one ,λg-l-class. We also point out that our results are closely related to the degree 0 Virasoro conjecture for a curve.展开更多
文摘We derive some quadratic recursion relations for some Hodge integrals by virtual localization and obtain many closed formulas. We apply our formulas to the local geometry of toric Fano surfaces in a Calabi-Yau threefold and compute some of the numbers $n_\beta ^g$ in Gopakumar-Vafa's formula for all g in this case.
文摘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 differen-tial 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 a generalization of the work in Liu and Wang[Commun.Math.Phys.346(1):143-190,2016]for the point case which solved a conjecture of Alexandrov.
文摘Hodge integrals over moduli space of stable curves play an important roles in understanding the topological properties of moduli space. ELSV formula connects the Hodge integrals with Hurwitz numbers, and the generating function of Hurwitz numbers satisfies the cut-and-join equation. Therefore, it is natural to consider how to use the cut-and-join equation for Hurwitz numbers to compute Hodge integrals which appear in ELSV formula. In this paper, at first, we will review the method introduced in Goulden et al.＇s paper to get the λg conjecture for Hodge integral. Through some variables transformation, the generating function of Hurwitz number becomes a symmetric polynomial which satisfies a symmetrized cut-and-join equation. By comparing the coefficients of the lowest degree term of both sides in this equation, we can get the ,λg conjecture. Then, in a similar way, we obtain our main result in this paper： a recursive formula for Hodge integral of type contains only one ,λg-l-class. We also point out that our results are closely related to the degree 0 Virasoro conjecture for a curve.
