A Change of Coordinates on the Large Phase Space of Quantum Cohomology

Abstract

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 prove that the potential functions associated to the tautological $\psi$ classes (the large phase space) and the $\kappa$ classes are related by a change of coordinates which generalizes a change of basis on the ring of symmetric functions. Our result is a generalization of the work of Manin--Zograf who studied the case where $V$ is a point. We utilize this change of variables to derive the topological recursion relations associated to the $\kappa$ classes from those associated to the $\psi$ classes.