A new method toward the Landau–Ginzburg/Calabi–Yau correspondence via quasi-maps

Abstract

The Landau-Ginzburg/Calabi-Yau correspondence claims that the Gromov-Witten invariant of the quintic Calabi-Yau 3-fold should be related to the Fan-Jarvis-Ruan-Witten invariant of the associated Landau-Ginzburg model via wall crossings. In this paper, we consider the stack of quasi-maps with a cosection and introduce sequences of stability conditions which enable us to interpolate between the moduli stack for Gromov-Witten invariants and the moduli stack for Fan-Jarvis-Ruan-Witten invariants.

Mixed-$\textrm{Spin-P}$ fields of Fermat polynomials

“…Here we mention the recent approaches for high genus LG/CY correspondence [CK,FJR2]. This paper is organized as follows.…”

Torus localization and wall crossing for cosection localized virtual cycles

“…For further applications, it seems desirable to have cosection localized analogues for torus localization formula, virtual pullback and wall crossing formulas. For instance, recently there arose a tremendous interest in the Landau-Ginzburg theory whose key invariants such as the Fan-Jarvis-Ruan-Witten invariants are defined algebro-geometrically by cosection localized virtual cycles ( [7,8]). The formulas proved in this paper will be useful in the theory of MSP fields developed in [4] tod study the Gromov-Witten invariants and the Fan-Jarvis-Ruan-Witten invariants of quintic Calabi-Yau threefolds.…”

The moduli space in the gauged linear sigma model

“…There are other choices of stability conditions that result in different moduli spaces. Please see [CLLL15,CK15] for examples.…”

“…And indeed, it is natural to view our GLSM-theory as a union of FJRW-theory with quasimap theory. However, it is possible to impose other stability conditions (see [CLLL15,CK15]).…”