Fukaya categories of blowups

Abstract

We compute the Fukaya category of the symplectic blowup of a compact rational symplectic manifold at a point in the following sense: Suppose a collection of Lagrangian branes satisfy Abouzaid's criterion for split-generation of a bulk-deformed Fukaya category of cleanly-intersecting Lagrangian branes. We show that for a small blow-up parameter, their inverse images in the blowup together with a collection of branes near the exceptional locus split-generate the Fukaya category of the blowup. This categorifies a result on quantum cohomology by Bayer and is an example of a more general conjectural description of the behavior of the Fukaya category under transitions occuring in the minimal model program, namely that mmp transitions generate additional summands.

126 pages. "eigenvector" -> "generalized eigenvector" in a few places

References in corpus (2)

• Holomorphic disks and the disk potential for a fibered Lagrangian
• Family Floer superpotential's critical values are eigenvalues of quantum product by $c_1$