Virtual cycles of stable (quasi-)maps with fields

Abstract

We generalize the results of Chang–Li, Kim–Oh and Chang–Li on the moduli of p-fields to the setting of (quasi-)maps to complete intersections in arbitrary smooth Deligne–Mumford stacks with projective coarse moduli. In particular, we show that the virtual cycle of stable (quasi-)maps to a complete intersection can be recovered by the cosection localized virtual cycle of the moduli of p-fields of the ambient space.