Journal
ADVANCES IN MATHEMATICS
Volume 397, Issue -, Pages -Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.aim.2021.108116
Keywords
Mirror symmetry; Fukaya categories; Homological mirror symmetry; Fukaya-Seidel categories; Knorrer periodicity; Symplectic geometry; Mirror symmetry; Fukaya categories; Homological mirror symmetry; Fukaya-Seidel categories; Knorrer periodicity; Symplectic geometry
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We explore the definition of the Fukaya category of a singular hypersurface proposed by Auroux and demonstrate its desirable properties. In addition, we discuss how this definition can be applied to homological mirror symmetry at various large complex structure limits.
We consider a definition of the Fukaya category of a singular hypersurface proposed by Auroux, given by localizing the Fukaya category of a nearby fiber at Seidel's natural transformation, and show that this possesses several desirable properties. Firstly, we prove an A-side analog of Orlov's derived Knorrer periodicity theorem by showing that Auroux' category is derived equivalent to the Fukaya-Seidel category of a higher-dimensional Landau-Ginzburg model. Secondly, we describe how this definition should imply homological mirror symmetry at various large complex structure limits, in the context of forthcoming work of Abouzaid-Auroux and Abouzaid-Gross-Siebert.(c) 2021 Elsevier Inc. All rights reserved.
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