The genus $0$ Gromov–Witten invariants of projective complete intersections

Abstract

We describe the structure of mirror formulas for genus $0$ Gromov–Witten invariants of projective complete intersections with any number of marked points and provide an explicit algorithm for obtaining the relevant structure coefficients. As an application, we give explicit closed formulas for the genus $0$ Gromov–Witten invariants of Calabi–Yau complete intersections with $3$ and $4$ constraints. The structural description alone suffices for some qualitative applications, such as vanishing results and the bounds on the growth of these invariants predicted by R Pandharipande. The resulting theorems suggest intriguing conjectures relating GW–invariants to the energy of pseudoholomorphic maps and the expected dimensions of their moduli spaces.