Algebraic Geometry Seminar
Tuesday, October 12, 1999, 4:15 pm, in JFB 102
Sasha Kabonov (ETH Zuerich)
Change of Coordinates on the Large Phase Space of Quantum Cohomology
(Joint work with T. Kimura) The Gromov-Witten invariants of a smooth, projective variety V, when twisted by the tautological classes on the moduli space of stable maps, give rise to a family of cohomological field theories and endow the base of the family with coordinates. We compare the potential functions associated to different choices of tautological classes, and prove that they are related by an explicit change of coordinates that resembles a change of basis on the ring of symmetric functions. This generalizes a result of Kaufmann--Manin--Zagier and Manin--Zograf who studied the case where V is a point.