Versality of the relative Fukaya category

Abstract

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.