On a proof of a conjecture of Mariño-Vafa on Hodge Integrals

Liu, Chiu-Chu Melissa; Liu, Kefeng; Zhou, Jian

doi:10.4310/mrl.2004.v11.n2.a9

Cited by 79 publications

(171 citation statements)

References 17 publications

(25 reference statements)

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“…For Calabi-Yau Hodge integrals, the results specialize to the Gopakumar-Mariño-Vafa formula proven in Liu-Liu-Zhou [21] and Okounkov-Pandharipande [29].…”

Section: Vertexmentioning

confidence: 98%

“…The 1-legged equivariant vertex (ii) contains the Calabi-Yau 1-legged vertex governed by the Gopakumar-Mariño-Vafa formula (see Liu-Liu-Zhou [21], Mariño-Vafa [23] and Okounkov-Pandharipande [29]) as a special case. The computation of the 1-legged equivariant vertex may be viewed as a Hodge integral result on the Gromov-Witten side or a vertex measure result on the Donaldson-Thomas side.…”

Section: Overviewmentioning

confidence: 99%

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The local Donaldson–Thomas theory of curves

2010

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“…For Calabi-Yau Hodge integrals, the results specialize to the Gopakumar-Mariño-Vafa formula proven in Liu-Liu-Zhou [21] and Okounkov-Pandharipande [29].…”

Section: Vertexmentioning

confidence: 98%

Section: Overviewmentioning

confidence: 99%

The local Donaldson–Thomas theory of curves

2010

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“…Special thanks are due to the organizers for their hospitality. A different proof the GMV formula can be found in [11], [12], see also [13].…”

Section: Acknowledgementsmentioning

confidence: 99%

Hodge integrals and invariants of the unknot

Okounkov

Pandharipande

2004

Geom. Topol.

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We prove the Gopakumar-Mariño-Vafa formula for special cubic Hodge integrals. The GMV formula arises from Chern-Simons/string duality applied to the unknot in the three sphere. The GMV formula is a q -analog of the ELSV formula for linear Hodge integrals. We find a system of bilinear localization equations relating linear and special cubic Hodge integrals. The GMV formula then follows easily from the ELSV formula. An operator form of the GMV formula is presented in the last section of the paper.

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“…[1], Marino and Vafa conjectured a formula on Hodge integrals which was proved in ref. [2]. Let Λ ∨ g (τ ) = τ g − τ g−1 λ 1 + · · · + (−1) g λ g denote the Chern polynomial of the dual bundle of the Hodge bundle.…”

Section: Introductionmentioning

confidence: 99%

A note on Marino-Vafa formula

2006

SCI CHINA SER A

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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 function of Hodge integrals via some combinatorial and algebraic data seemingly unrelated to these apriori algebraic geometric objects. We prove in this paper by directly expanding the formula and estimating the involved terms carefully that except a specific type all the other Hodge integrals involving up to three Hodge classes can be calculated from this formula. This implies that amazingly rich information about moduli spaces and Gromov-Witten invariants is encoded in this complicated formula. We also give some low genus examples which agree with the previous results in literature. Proofs and calculations are elementary as long as one accepts Mumford relations on the reductions of products of Hodge classes.

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On a proof of a conjecture of Mariño-Vafa on Hodge Integrals

Abstract: Abstract. We outline a proof of a remarkable formula for Hodge integrals conjectured by Mariño and Vafa [25] based on large N duality.

Cited by 79 publications

References 17 publications

The local Donaldson–Thomas theory of curves

The local Donaldson–Thomas theory of curves

Hodge integrals and invariants of the unknot

A note on Marino-Vafa formula

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