Speculations on homological mirror symmetry for hypersurfaces in $({\mathbb{C}}^{\ast }{)}^n$

Abstract

Given an algebraic hypersurface $H=f^{-1}(0)$ in $({\mathbb{C}}^{\ast }{)}^n$, homological mirror symmetry relates the wrapped Fukaya category of $H$ to the derived category of singularities of the mirror Landau-Ginzburg model. We propose an enriched version of this picture which also features the wrapped Fukaya category of the complement $({\mathbb{C}}^{\ast }{)}^n\setminus H$ and the Fukaya-Seidel category of the Landau-Ginzburg model $(({\mathbb{C}}^{\ast }{)}^n,f)$. We illustrate our speculations on simple examples, and sketch a proof of homological mirror symmetry for higher-dimensional pairs of pants.

45 pages

References in corpus (2)

• Symplectic cohomology and duality for the wrapped Fukaya category
• Homological mirror symmetry for open Riemann surfaces from pair-of-pants decompositions

Cited by in corpus (1)

• SYZ for index 1 Fano hypersurfaces in projective space