It is well-known that genus zero Gromov-Witten invariants of a subvariety Z?X can be recovered, in many cases, from invariants of X by studying obstruction bundles. Unfortunately, this result fails for higher genus invariants as well as for orbifold invariants. The moduli space of stable maps with p-fields was first introduced by Huai-Liang Chang and Jun Li, who proved a comparison theorem relating stable maps with p-fields to higher genus Gromov-Witten invariants of the quintic threefold. The original construction has since seen various generalizations and applications.
I will give some background and discuss a general version of the construction of stable maps with p-fields and of the comparison theorem for orbifold GW invariants.
