Hodge integrals and Gromov-Witten theory

@article{Faber1998HodgeIA,
  title={Hodge integrals and Gromov-Witten theory},
  author={Carel Faber and Rahul Pandharipande},
  journal={Inventiones mathematicae},
  year={1998},
  volume={139},
  pages={173-199}
}
Integrals of the Chern classes of the Hodge bundle in Gromov-Witten theory are studied. We find a universal system of differential equations which determines the generating function of these integrals from the standard descendent potential (for any target X). We use virtual localization and classical degeneracy calculations to find trigonometric closed form solutions for special Hodge integrals over the moduli space of pointed curves. These formulas are applied to two computations in Gromov… 
View on Springer
arxiv.org
494 Citations
Highly Influential Citations
48
Background Citations
155
Methods Citations
116
Results Citations
14

494 Citations

Connecting Hodge Integrals to Gromov–Witten Invariants by Virasoro Operators

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…

The local Gromov-Witten theory of curves

The local Gromov-Witten theory of curves is solved by localization and degeneration methods. Localization is used for the exact evalu- ation of basic integrals in the local Gromov-Witten theory of P…

A note on Marino-Vafa formula

Hodge integrals over moduli spaces of curves appear naturally during the localization procedure in computation of Gromov-Witten invariants. A remarkable formula of Marino-Vafa expresses a generation…

TOPOLOGICAL RELATIONS ON WITTEN-KONTSEVICH AND HODGE POTENTIALS

Let Mg;n denote the moduli space of genus g stable alge- braic curves with n marked points. It carries the Mumford cohomology classesi. A homology class in H�(Mg;n) is said to be �-zero if the…

A relative Riemann-Hurwitz theorem, the Hurwitz-Hodge bundle, and orbifold Gromov-Witten theory

We provide a formula describing the G-module structure of the Hurwitz-Hodge bundle for admissible G-covers in terms of the Hodge bundle of the base curve, and more generally, for describing the…

A Klein TQFT: the local Real Gromov-Witten theory of curves

Logarithmic series and Hodge integrals in the tautological ring. With an appendix by Don Zagier.

0.1. Overview. Let Mg be the moduli space of Deligne–Mumford stable curves of genus g ≥ 2. The study of the Chow ring of the moduli space of curves was initiated by Mumford in [Mu]. In the past two…

The Gromov–Witten Potential of A Point, Hurwitz Numbers, and Hodge Integrals

Hurwitz numbers, which count certain covers of the projective line (or, equivalently, factorizations of permutations into transpositions), have been extensively studied for over a century. The…

Quantum Riemann–Roch, Lefschetz and Serre

Given a holomorphic vector bundle E over a compact Kahler manifold X, one defines twisted Gromov-Witten invariants of X to be intersection numbers in moduli spaces of stable maps f :Σ → X with the…

Degree zero Gromov--Witten invariants for smooth curves

. For a smooth projective curve, we derive a closed formula for the generating series of its Gromov–Witten invariants in genus g and degree zero. It is known that the calculation of these invariants…
...

References

SHOWING 1-10 OF 23 REFERENCES

Counting higher genus curves in a Calabi-Yau manifold

Virasoro constraints and the Chern classes of the Hodge bundle

Quantum cohomology and Virasoro algebra

Towards an Enumerative Geometry of the Moduli Space of Curves

The goal of this paper is to formulate and to begin an exploration of the enumerative geometry of the set of all curves of arbitrary genus g. By this we mean setting up a Chow ring for the moduli…

Topological field theory and rational curves

We analyze the quantum field theory corresponding to a string propagating on a Calabi-Yau threefold. This theory naturally leads to the consideration of Witten's topological non-linear σ-model and…

M theory and topological strings. 2.

The $R^2 F^{2g-2}$ terms of Type IIA strings on Calabi-Yau 3-folds, which are given by the corresponding topological string amplitudes (a worldsheet instanton sum for all genera), are shown to have a…

Virtual moduli cycles and Gromov-Witten invariants of algebraic varieties

We introduce a method of constructing the virtual cycle of any scheme associated with a tangent-obstruction complex. We apply this method to constructing the virtual moduli cycle of the moduli of…

Localization of virtual classes

We prove a localization formula for virtual fundamental classes in the context of torus equivariant perfect obstruction theories. As an application, the higher genus Gromov-Witten invariants of…

Frobenius manifolds and Virasoro constraints

Abstract. For an arbitrary Frobenius manifold, a system of Virasoro constraints is constructed. In the semisimple case these constraints are proved to hold true in the genus one approximation. In…

Generating Functions in Algebraic Geometry and Sums Over Trees

We calculate generating functions for the Poincare polynomials of moduli spaces of pointed curves of genus zero and of Configuration Spaces of Fulton and MacPherson. We also prove that contributions…