Fukaya A_\infty-structures associated to Lefschetz fibrations. II 1/2
Paul Seidel
TL;DR
This paper explores a version of the relative Fukaya category linked to anticanonical Lefschetz pencils, aiming to connect symplectic geometry with enumerative geometry and ultimately determine the Fukaya category of Calabi-Yau hypersurfaces.
Contribution
It introduces a new approach to studying Fukaya categories associated with Lefschetz pencils, highlighting connections to enumerative geometry and proposing conjectural results.
Findings
Establishes connections between Fukaya categories and enumerative geometry.
Proposes methods to determine Fukaya categories of Calabi-Yau hypersurfaces.
Announces results and conjectures related to these categories.
Abstract
We consider a version of the relative Fukaya category for anticanonical Lefschetz pencils. There are direct connections between the behaviour of this category and enumerative geometry: some of these are results announced here, others remain conjectural. The ultimate aim of this approach is to determine the Fukaya category of the Calabi-Yau hypersurfaces that constitute the pencil.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology