Constructing the relative Fukaya category

2022/03/29 by Timothy Perutz, Nick Sheridan, Perutz, Timothy +1 · 4 citations
Mathematics · #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2203.15482

openalex publication_date 2022/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We give a definition of Seidel's `relative Fukaya category', for a smooth complex projective variety, under a semipositivity assumption. We use the Cieliebak--Mohnke approach to transversality via stabilizing divisors. Two features of our construction are noteworthy: that we work relative to a normal crossings divisor that supports an effective ample divisor but need not have ample components; and that our relative Fukaya category is linear over a certain ring of multivariate power series with integer coefficients.

Cited by

• Symplectic cohomology with support and aspherical perturbations
• Plumbings of lens spaces and crepant resolutions of compound A_n singularities
• The cyclic open--closed map and variations of Hodge structures
• Lagrangian Floer theory, from geometry to algebra and back again

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