Fukaya category for Landau-Ginzburg orbifolds

For a weighted homogeneous polynomial and a choice of a diagonal symmetry group, we define a new Fukaya category for a Landau-Ginzburg orbifold (of Fano or Calabi-Yau type). The construction is based on the wrapped Fukaya category of its Milnor fiber together with the monodromy of the singularity, a...

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Bibliographic Details
Published inarXiv.org
Main Authors Cheol-Hyun Cho, Choa, Dongwook, Jeong, Wonbo
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 29.09.2022
Subjects
Group theory
Homology
Hyperspaces
Polynomials
Singularities
Symmetry
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Summary:For a weighted homogeneous polynomial and a choice of a diagonal symmetry group, we define a new Fukaya category for a Landau-Ginzburg orbifold (of Fano or Calabi-Yau type). The construction is based on the wrapped Fukaya category of its Milnor fiber together with the monodromy of the singularity, and it is analogous to the variation operator in singularity theory. The new \(\AI\)-structure is constructed using popsicle maps with interior insertions of the monodromy orbit. This requires new compactifications of popsicle moduli spaces where conformal structures of some of the spheres and discs are aligned due to the popsicle structures. In particular, codimension one popsicle sphere bubbles might exist and become obstructions to define the \(\AI\)-structure. For log Fano and Calabi-Yau cases, we show that the sphere bubbles do not arise from action and degree estimates, together with the computation of indices of twisted Reeb orbits for Milnor fiber quotients.
ISSN:2331-8422