Reconstruction theorems for Gromov-Witten invariants

摘要

We prove a Reconstruction Theorem for (ordinary) Gromov-Witten invariants which improves the First Reconstruction Theorem of Kontsevich and Manin for manifolds whose Picard number is not one. In some cases our Reconstruction Theorem gives 1-point reconstruction. We discuss some interesting examples in detail, and finally we describe four applications: rational surfaces, Fano threefolds, the blow-up of the projective space along a linear subspace, and the non-Fano moduli space of curves (M) over bar (0.6).