Homological Mirror Symmetry and Fukaya Categories of Calabi-Yau Hypersurfaces in Toric Varieties

This monograph establishes a rigorous categorical equivalence between the derived category of coherent sheaves on a Calabi-Yau hypersurface X within a Gorenstein toric variety V and the derived Fukaya category of its mirror Landau-Ginzburg model (Y, W). We invoke the Batyrev-Borisov construction to define the mirror pairs via reflexive polytopes and . The core analysis focuses on the A-structure of the Fukaya category F(Y), explicitly computing the structural maps k via moduli spaces of pseudo-holomorphic disks with Lagrangian boundary conditions. We demonstrate that the split-closure of the derived Fukaya category, DF(Y), is triangulated equivalent to Db Coh(X) by constructing a faithful A-functor mapping the structure sheaf OX to a Lagrangian section of the SYZ fibration. Furthermore, we address the non-archimedean convergence of the instanton corrections over the Novikov ring nov, ensuring the deformation invariance of the Floer cohomology groups under Hamiltonian isotopies.