Multipoint series of Gromov-Witten invariants of ℂℙ1

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)159-170
Number of pages12
JournalLetters in Mathematical Physics
Issue number2
StatePublished - Nov 2002


  • Gromov-Witten invariants
  • Toda lattice

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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