Higher-genus wall-crossing in Landau–Ginzburg theory

Abstract

For a Fermat quasi-homogeneous polynomial, we study the associated weighted Fan-Jarvis-Ruan-Witten theory with narrow insertions. We prove a wall-crossing formula in all genera via localization on a master space, which is constructed by introducing an additional tangent vector to the moduli problem. This is a Landau-Ginzburg theory analogue of the higher-genus quasi-map wall-crossing formula proved by Ciocan-Fontanine and Kim. It generalizes the genus-0 result by Ross-Ruan and the genus-1 result by Guo-Ross.It is easy to see that the isomorphism is compatible with the cosections.Then we consider the τ * T M term of the distinguished triangle (15). By Lemma 13, the fixed part is τ * T F 1/r J . Moreover, since pr 1 isétale, we have T F 1/r J ∼ = pr * 1 T M 1/r g,γ J . This finishes the proof that pr * 1 ([M 1/r,ϕ g,γJ ] vir loc ) = [F ϕ J ] vir loc .2 The C * -action on L is only well-defined up to µ µ µr. Nevertheless we can compose the action with the r-th power map C * → C * so that it is well-defined. 1/r 0,γ . However, we can pushforward everything to a point instead. For any non-negative integer c this gives (28) J ψ c φ a , µ + J (−ψ)|(φ bj ) j ∈J 0 0,2|(n−|J|) = µ B (z) z −c−1 ,

Quasimap wall-crossing for GIT quotients

“…(3) During the preparation of this paper, the author learned that Jun Wang independently proved [41] the genus-0 wall-crossing formula for hyper-surfaces in toric stacks for which convexity can fail, and used that to prove a mirror theorem. 1 Motivated by the LG/CY correspondence, there are also similar wall-crossing results on the LG side [16,43]. The method in this paper also works in the setting of K-theoretic Gromov-Witten invariants.…”