## Abstract

We derive explicit formulas for the multipoint series of ℂℙ^{1} 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 ℂℙ^{1}. We also obtain explicit formulas for the Hodge integrals ∫_{M̄g,n} ψ^{k1}_{1} . . . ψ^{kn}_{n}λ_{g-i}, in the cases i = 0 and 1.

Original language | English |
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Pages (from-to) | 159-170 |

Number of pages | 12 |

Journal | Letters in Mathematical Physics |

Volume | 62 |

Issue number | 2 |

DOIs | |

Publication status | Published - Nov 2002 |

Externally published | Yes |

## Keywords

- Gromov-Witten invariants
- Toda lattice

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