2017/05/18 by Auroux, Denis
#Algebraic Geometry (math.AG) #FOS: Mathematics #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.1705.06667
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.