Reichelt, Thomas; Sevenheck, Christian Non-affine Landau-Ginzburg models and intersection cohomology. (Modèles de Landau-Ginzburg non affines et cohomologie d’intersection.) (English. French summary) Zbl 1395.14033 Ann. Sci. Éc. Norm. Supér. (4) 50, No. 3, 665-753 (2017). The paper aims at constructing mirror models for complete intersections in smooth toric varieties in the case when these subvarieties have a numerically effective anticanonical bundle. Particular cases of such are toric Fano manifolds, whose mirror is usually described by oscillating integrals defined by Laurent polynomials, and Calabi-Yau hypersurfaces in toric Fano manifolds. Both occur as special cases of non-affine Landau-Ginzburg models (LGMs). The authors construct LGMs for numerically effective intersections of toric manifolds as partial compactifications of families of Laurent polynomials. They show that the quantum \(\mathcal{D}\)-module of the ambient part of the cohomology of the submanifold is isomorphic to an intersection cohomology \(\mathcal{D}\)-module defined from the partial compactification. They deduce Hodge properties of these differential systems. Reviewer: Vladimir P. Kostov (Nice) Cited in 1 ReviewCited in 7 Documents MSC: 14J33 Mirror symmetry (algebro-geometric aspects) 14M25 Toric varieties, Newton polyhedra, Okounkov bodies 32S40 Monodromy; relations with differential equations and \(D\)-modules (complex-analytic aspects) 32S60 Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects) 14D07 Variation of Hodge structures (algebro-geometric aspects) 34Mxx Ordinary differential equations in the complex domain 53D45 Gromov-Witten invariants, quantum cohomology, Frobenius manifolds Keywords:Gauss-Manin system; hypergeometric \(\mathcal{D}\)-module; toric variety; intersection cohomology; Radon transformation; Landau-Ginzburg model; Calabi-Yau hypersurface PDFBibTeX XMLCite \textit{T. Reichelt} and \textit{C. Sevenheck}, Ann. Sci. Éc. Norm. Supér. (4) 50, No. 3, 665--753 (2017; Zbl 1395.14033) Full Text: DOI arXiv Link