Speculations on homological mirror symmetry for hypersurfaces in (C*)ⁿ
Auroux, Denis
Original · EN
Given an algebraic hypersurface H=f⁻¹(0) in (C*)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 (C*)ⁿ H and the Fukaya-Seidel category of the Landau-Ginzburg model ((C*)ⁿ,f). We illustrate our speculations on simple examples, and sketch a proof of homological mirror symmetry for higher-dimensional pairs of pants.
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