Virasoro constraints and the Chern classes of the Hodge bundle

E. Getzler; R. Pandharipande

doi:10.1016/S0550-3213(98)00517-3

Virasoro constraints and the Chern classes of the Hodge bundle

E. Getzler^*, R. Pandharipande

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

68 Scopus citations

Abstract

We analyse the consequences of the Virasoro conjecture of Eguchi, Hori and Xiong for Gromov-Witten invariants, in the case of zero degree maps to the manifolds ℙ¹ and ℙ² (or more generally, smooth projective curves and smooth simply connected protective surfaces). We obtain predictions involving intersections of psi and lambda classes on M̄_g,n. In particular, we show that the Virasoro conjecture for ℙ² implies the numerical part of Faber's conjecture on the tautological Chow ring of M_g.

Original language	English (US)
Pages (from-to)	701-714
Number of pages	14
Journal	Nuclear Physics B
Volume	530
Issue number	3
DOIs	https://doi.org/10.1016/S0550-3213(98)00517-3
State	Published - Oct 19 1998

Keywords

Gromov-Witten invariants
Topological gravity
Virasoro conjecture

ASJC Scopus subject areas

Nuclear and High Energy Physics

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10.1016/S0550-3213(98)00517-3

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T1 - Virasoro constraints and the Chern classes of the Hodge bundle

AU - Getzler, E.

AU - Pandharipande, R.

PY - 1998/10/19

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N2 - We analyse the consequences of the Virasoro conjecture of Eguchi, Hori and Xiong for Gromov-Witten invariants, in the case of zero degree maps to the manifolds ℙ1 and ℙ2 (or more generally, smooth projective curves and smooth simply connected protective surfaces). We obtain predictions involving intersections of psi and lambda classes on M̄g,n. In particular, we show that the Virasoro conjecture for ℙ2 implies the numerical part of Faber's conjecture on the tautological Chow ring of Mg.

AB - We analyse the consequences of the Virasoro conjecture of Eguchi, Hori and Xiong for Gromov-Witten invariants, in the case of zero degree maps to the manifolds ℙ1 and ℙ2 (or more generally, smooth projective curves and smooth simply connected protective surfaces). We obtain predictions involving intersections of psi and lambda classes on M̄g,n. In particular, we show that the Virasoro conjecture for ℙ2 implies the numerical part of Faber's conjecture on the tautological Chow ring of Mg.

KW - Gromov-Witten invariants

KW - Topological gravity

KW - Virasoro conjecture

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SN - 0550-3213

VL - 530

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EP - 714

JO - Nuclear Physics B

JF - Nuclear Physics B

IS - 3

ER -

Virasoro constraints and the Chern classes of the Hodge bundle

Abstract

Keywords

ASJC Scopus subject areas

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