Non-affine Landau-Ginzburg models and intersection cohomology - Reichelt, Thomas; Sevenheck, Christian (Annales scientifiques de l'Ecole Normale Supérieure, 2017)
We construct Landau-Ginzburg models for numerically effective complete intersections in toric manifolds as partial compactifications of families of Laurent polynomials. We show a mirror statement saying that the quantum D-module of the ambient part of the cohomology of the submanifold is isomorphic to an intersection cohomology D-module defined from this partial compactification and we deduce Hodge properties of these differential systems.