Generating the Fukaya categories of compact toric varieties
Jack Smith

TL;DR
This paper explicitly constructs objects in the Fukaya category of compact toric varieties, demonstrating how the Kodaira-Spencer isomorphism factors through the closed-open map and establishing split-generation of certain summands.
Contribution
It provides an explicit construction linking the Kodaira-Spencer isomorphism to the closed-open map, proving split-generation of Fukaya category summands for compact toric varieties.
Findings
The Hochschild cohomology injects into the Fukaya category.
Explicit objects are constructed for each summand.
Split-generation of Fukaya categories is established.
Abstract
Let be a compact toric variety. The quantum cohomology of decomposes as a direct sum, and associated to each summand is a toric fibre with rank local system. By building an explicit twisted-complex-like object, we show that on the Kodaira-Spencer isomorphism of Fukaya-Oh-Ohta-Ono factors through the closed-open string map to the Hochschild cohomology of . We deduce that the latter is injective and hence, assuming an appropriate version of Abouzaid's criterion, that split generates the corresponding summand of the Fukaya category.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Combinatorial Mathematics · Algebraic Geometry and Number Theory
