Gromov-Witten invariants of target curves via Symplectic Field Theory

Details Gromov-Witten invariants of target curves via Symplectic Field Theory Gromov-Witten invariants of target curves via Symplectic Field Theory

2007-09-18

arxiv.org/abs/0709.2860v1

J.Geom.Phys.58:931-941,2008

Mathematics

Symplectic Geometry

13 pages

Scientific paper

10.1016/j.geomphys.2008.02.012

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. This amounts to impose (and possibly solve) different kinds of Schroedinger equations related to some quantization of the dispersionless KdV hierarchy. In particular we find very explicit formulas for the Gromov-Witten invariants of low degree of P1 with descendants of the Kaehler class.

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