Gromov–Witten invariant

Summary

A Gromov–Witten invariant is a rational number that counts curves in a smooth projective variety or a symplectic manifold. The curves have a given genus and homology class, and they pass through given cycles. It is defined by integrating cohomology classes over the virtual fundamental class of a moduli space of stable maps. These invariants solve classical questions of enumerative geometry, they define quantum cohomology, and they are one side of mirror symmetry.