  Given an algebraic hypersurface $H=f^{-1}(0)$ in $(\mathbb{C}^*)^n$,
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 $(\mathbb{C}^*)^n\setminus H$ and the
Fukaya-Seidel category of the Landau-Ginzburg model $((\mathbb{C}^*)^n,f)$. We
illustrate our speculations on simple examples, and sketch a proof of
homological mirror symmetry for higher-dimensional pairs of pants.
