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.
- Gromov-Witten invariants
- Toda lattice
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics