SYZ for index 1 Fano hypersurfaces in projective space

2021/10/20 by Alami, Mohamed El
#Algebraic Geometry (math.AG) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2110.10728

Abstract

We study homological mirror symmetry of the singular hypersurface X₀=V(tⁿ⁺¹-x₀\dotsi x_n)⊆ℙⁿ⁺¹. Following an SYZ type approach, we produce an LG-model, whose Fukaya-Seidel category recovers line bundles on X₀. 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 ℙⁿ⁺¹, without bounding co-chains.

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