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Versality of the relative Fukaya category

Nick Sheridan

Geometry & Topology 24 (2020) 747–884

Seidel introduced the notion of a Fukaya category “relative to an ample divisor”, explained that it is a deformation of the Fukaya category of the affine variety that is the complement of the divisor, and showed how the relevant deformation theory is controlled by the symplectic cohomology of the complement. We elaborate on Seidel’s definition of the relative Fukaya category, and give a criterion under which the deformation is versal.

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Relative Fukaya category, mirror symmetry, versality, deformation theory
Mathematical Subject Classification 2010
Primary: 53D37
Received: 25 January 2018
Revised: 26 April 2019
Accepted: 6 August 2019
Published: 23 September 2020
Proposed: Yasha Eliashberg
Seconded: Ciprian Manolescu, Ralph Cohen
Nick Sheridan
School of Mathematics
University of Edinburgh
United Kingdom