SYZ for index 1 Fano hypersurfaces in projective space
Mohamed El Alami

TL;DR
This paper investigates homological mirror symmetry for a specific singular Fano hypersurface using SYZ methods, producing an LG-model that recovers line bundles and confirming a conjecture about Fukaya categories.
Contribution
It introduces an SYZ-based approach to construct an LG-model for the hypersurface, linking Fukaya-Seidel categories to line bundles and resolving a conjecture on Fukaya category generation.
Findings
Constructed an LG-model via SYZ for the hypersurface
Fukaya-Seidel category recovers line bundles on the hypersurface
Confirmed Sheridan's conjecture on Fukaya category generation
Abstract
We study homological mirror symmetry of the singular hypersurface . Following an SYZ type approach, we produce an LG-model, whose Fukaya-Seidel category recovers line bundles on . As a byproduct of our approach, we answer a conjecture of N.Sheridan about generating the small component of the Fukaya category of the smooth index 1 Fano hypersurface in , without bounding co-chains.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Nonlinear Waves and Solitons
