Topological recursion relations and Gromov-Witten invariants in higher genus

Details Topological recursion relations and Gromov-Witten invariants in higher genus Topological recursion relations and Gromov-Witten invariants in higher genus

2003-05-26

arxiv.org/abs/math/0305361v1

Mathematics

Algebraic Geometry

20 pages, computer program available on request

Scientific paper

We state and prove a topological recursion relation that expresses any genus-g Gromov-Witten invariant of a projective manifold with at least a (3g-1)-st power of a cotangent line class in terms of invariants with fewer cotangent line classes. For projective spaces, we prove that these relations together with the Virasoro conditions are sufficient to calculate the full Gromov-Witten potential. This gives the first computationally feasible way to determine the higher genus Gromov-Witten invariants of projective spaces.

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