Gromov-Witten Invariants of Stable Maps with Fields

Abstract

Abstract. We construct the Gromov-Witten invariants of moduli of stable morphisms to P 4 with fields. This is the all genus mathematical theory of the Guffin-Sharpe-Witten model, and is a modified twisted Gromov-Witten invariants of P 4 . These invariants are constructed using the cosection localization of Kiem-Li, an algebro-geometric analogue of Witten's perturbed equations in Landau-Ginzburg theory. We prove that these invariants coincide, up to sign, with the Gromov-Witten invariants of quintics.

Reduced invariants from cuspidal maps

“…We are finally able to study the cone C Z p / XP . This is going to be a word-byword repetition of the arguments in [CL12].…”

A Vanishing Associated With Irregular MSP Fields

“…be their respective virtual normal cones [BF, LT]. Applying argument analogous to [CL2,Coro. 2.9] (see also [KKP,Prop.…”

The moduli space in the gauged linear sigma model

“…, b K )}. And (∞, ϑ 0 )-stable LGquasimaps to X geom are stable maps to X F with p-fields, studied in [CL11,CLL13].…”

“…Both theories have the same moduli spaces, but the virtual cycle constructions are different. For ε = ∞, Chang-Li [CL11] proved the equivalence using a sophisticated degeneration argument. A similar argument probably works for other ε-theories.…”