Versality of the relative Fukaya category

TL;DR

This paper explores the relative Fukaya category, providing a criterion for its versality and elaborating on its deformation theory controlled by symplectic cohomology, advancing understanding in symplectic geometry.

Contribution

It refines Seidel's definition of the relative Fukaya category and introduces a criterion for its versality, deepening the theoretical framework.

Findings

Established a criterion for versality of the relative Fukaya category

Clarified the deformation control via symplectic cohomology

Extended the understanding of Fukaya categories relative to divisors

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.