Gromov-Witten invariants of target curves via Symplectic Field Theory

摘要

We compute the Gromov-Witten potential at all genera of target smooth Riemann surfaces using Symplectic Field Theory techniques and establish differential equations for the full descendant potential. We need to impose (and possibly solve) different kinds of Schrodinger equations related to some quantization of the dispersionless KdV hierarchy. In particular, we find explicit formulas for the Gromov-Witten invariants of low degree of P-1 with descendants of the Kahler class.