Topological recursion relations and Gromov-Witten invariants in higher genus

Abstract

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.

20 pages, computer program available on request

References in corpus (2)

• Quantum Cohomology and Virasoro Algebra
• Topological recursion relations in genus 2

Cited by in corpus (10)

• A Genus-3 Topological Recursion Relation
• Chow rings of stacks of prestable curves I
• A Fock space approach to Severi degrees
• The n-point functions for intersection numbers on moduli spaces of curves
• Descendent integrals and tautological rings of moduli spaces of curves
• A topological view of Gromov-Witten theory
• A Remark on Gromov-Witten Invariants of Quintic Threefold
• Labeled floor diagrams for plane curves
• A proof of the Faber intersection number conjecture
• Topological Recursion Relations on ${\bar{\mathcal{M}}}_{3,2}$