摘要

We prove a closed formula for an excess integral over the moduli space of stable maps from genus one, unmarked curves to the projective space P-r of degree d for any positive integers r and d. The result generalizes the multiple cover formula for P-1. We also show that any simple IPr flop preserves the theory of arbitrary-genus Gromov-Witten invariants in exceptional curve classes.

  • 出版日期2012