Constructing the relative Fukaya category

We give a definition of Seidel’s ‘relative Fukaya category’, for a smooth complex projective variety relative to a simple normal crossings divisor, 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 which 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.

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Received 3 May 2022

Received revised 31 January 2023

Accepted 5 April 2023

Published 4 June 2024