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Non-affine Landau-Ginzburg models and intersection cohomology (1210.6527v4)
Published 24 Oct 2012 in math.AG
Abstract: 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.