Multipoint series of Gromov-Witten invariants of ℂℙ1

E. Getzler; A. Okounkov; R. Pandharipande

doi:10.1023/A:1021698309415

Multipoint series of Gromov-Witten invariants of ℂℙ¹

E. Getzler^*, A. Okounkov, R. Pandharipande

^*Corresponding author for this work

Mathematics

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

11 Scopus citations

Abstract

We derive explicit formulas for the multipoint series of ℂℙ¹ in degree 0 from the Toda hierarchy, using the recursions of the Toda hierarchy. The Toda equation then yields inductive formulas for the higher degree multipoint series of ℂℙ¹. We also obtain explicit formulas for the Hodge integrals ∫_M̄g,n ψ^k1₁ . . . ψ^kn_nλ_g-i, in the cases i = 0 and 1.

Original language	English (US)
Pages (from-to)	159-170
Number of pages	12
Journal	Letters in Mathematical Physics
Volume	62
Issue number	2
DOIs	https://doi.org/10.1023/A:1021698309415
State	Published - Nov 2002

Keywords

Gromov-Witten invariants
Toda lattice

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

Access to Document

10.1023/A:1021698309415

Cite this

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title = "Multipoint series of Gromov-Witten invariants of ℂℙ1",

abstract = "We derive explicit formulas for the multipoint series of ℂℙ1 in degree 0 from the Toda hierarchy, using the recursions of the Toda hierarchy. The Toda equation then yields inductive formulas for the higher degree multipoint series of ℂℙ1. We also obtain explicit formulas for the Hodge integrals ∫{\=M}g,n ψk11 . . . ψknnλg-i, in the cases i = 0 and 1.",

keywords = "Gromov-Witten invariants, Toda lattice",

author = "E. Getzler and A. Okounkov and R. Pandharipande",

note = "Funding Information: E.G. was partially supported by DMS-0072508, A.O. by DMS-0096246 and fellowships from the Sloan and Packard foundations, and R.P. by DMS-0071473 and fellowships from the Sloan and Packard foundations.",

year = "2002",

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doi = "10.1023/A:1021698309415",

language = "English (US)",

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T1 - Multipoint series of Gromov-Witten invariants of ℂℙ1

AU - Getzler, E.

AU - Okounkov, A.

AU - Pandharipande, R.

N1 - Funding Information: E.G. was partially supported by DMS-0072508, A.O. by DMS-0096246 and fellowships from the Sloan and Packard foundations, and R.P. by DMS-0071473 and fellowships from the Sloan and Packard foundations.

PY - 2002/11

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N2 - We derive explicit formulas for the multipoint series of ℂℙ1 in degree 0 from the Toda hierarchy, using the recursions of the Toda hierarchy. The Toda equation then yields inductive formulas for the higher degree multipoint series of ℂℙ1. We also obtain explicit formulas for the Hodge integrals ∫M̄g,n ψk11 . . . ψknnλg-i, in the cases i = 0 and 1.

AB - We derive explicit formulas for the multipoint series of ℂℙ1 in degree 0 from the Toda hierarchy, using the recursions of the Toda hierarchy. The Toda equation then yields inductive formulas for the higher degree multipoint series of ℂℙ1. We also obtain explicit formulas for the Hodge integrals ∫M̄g,n ψk11 . . . ψknnλg-i, in the cases i = 0 and 1.

KW - Gromov-Witten invariants

KW - Toda lattice

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