• Corpus ID: 17535031

Hodge integrals, Hurwitz numbers, and Symmetric Groups

@article{Zhou2003HodgeIH,
  title={Hodge integrals, Hurwitz numbers, and Symmetric Groups},
  author={Jian Zhou},
  journal={arXiv: Algebraic Geometry},
  year={2003}
}
  • Jian Zhou
  • Published 4 August 2003
  • Mathematics
  • arXiv: Algebraic Geometry
We prove some combinatorial results related to a formula on Hodge integrals conjectured by Mari\~no and Vafa. These results play important roles in the proof and applications of this formula by the author jointly with Chiu-Chu Melissa Liu and Kefeng Liu. We also compare with some related results on Hurwitz numbers and obtain some closed expressions for the generating series of Hurwitz numbers and the related Hodge integrals. 
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39 Citations
Background Citations
4
Methods Citations
1

39 Citations

A Conjecture on Hodge Integrals
We propose a conjectural formula expressing the generating series of some Hodge integrals in terms of representation theory of Kac-Moody algebras. Such generating series appear in calculations of…
A Proof of a Conjecture of Marino-Vafa on Hodge Integrals
We prove a remarkable formula for Hodge integrals conjectured by Marino and Vafa based on large N duality, using functorial virtual localization on certain moduli spaces of relative stable morphisms.
Hodge Integrals and Integrable Hierarchies
We show that the generating series of some Hodge integrals involving one or two partitions are τ-functions of the KP hierarchy or the 2-Toda hierarchy, respectively. We also reformulate the results…
Some Results of the Mari˜no -vafa Formula
In this paper we derive some new Hodge integral identities by taking limits of the Mariño-Vafa formula. These identities include the formula of λ 1 λ g-integral on M g,1 , the vanishing result of λ g…
KP hierarchy for Hurwitz-type cohomological field theories
Abstract. We generalise a result of Kazarian regarding Kadomtsev-Petviashvili integrability for single Hodge integrals to general cohomological field theories related to Hurwitz-type counting…
Curve counting and instanton counting
We prove some combinatorial results required for the proof of the following conjecture of Nekrasov: The generating function of closed string invariants in local Calabi-Yau geometries obtained by…
A formula of two-partition Hodge integrals
JMg,n where tpi = ci(L?) is the first Chern class of L?, and Xj = Cj(E) is the j-th Chern class of the Hodge bundle. The study of Hodge integrals is an important part of intersection theory on Mg,n>…
Polynomial recursion formula for linear Hodge integrals
We establish a polynomial recursion formula for linear Hodge integrals. It is obtained as the Laplace transform of the cut-and-join equation for the simple Hurwitz numbers. We show that the recursion…
Computing Hodge Integrals with One Λ-class
where ψi is the first Chern class of the cotangent line bundle at the i-th marked point, and λ1, · · · , λg are the Chern classes of the Hodge bundle. Hodge integrals arise naturally in the…
Quantum curves for simple Hurwitz numbers of an arbitrary base curve
Various generating functions of simple Hurwitz numbers of the projective line are known to satisfy many properties. They include a heat equation, the Eynard-Orantin topological recursion, an…
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References

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A Proof of a Conjecture of Marino-Vafa on Hodge Integrals
We prove a remarkable formula for Hodge integrals conjectured by Marino and Vafa based on large N duality, using functorial virtual localization on certain moduli spaces of relative stable morphisms.
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