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.

arXiv comment45 pages

References in corpus (6)

• Triangulated categories of singularities and D-branes in Landau-Ginzburg models
• Homological Mirror Symmetry for Calabi-Yau hypersurfaces in projective space
• Symplectic cohomology and duality for the wrapped Fukaya category
• Homogeneous coordinate rings and mirror symmetry for toric varieties
• Wrapped microlocal sheaves on pairs of pants
• Homological mirror symmetry for open Riemann surfaces from pair-of-pants decompositions

Cited by in corpus (2)

• Monodromy of monomially admissible Fukaya-Seidel categories mirror to toric varieties
• SYZ for index 1 Fano hypersurfaces in projective space