an:06760100
Zbl 1395.14033
Reichelt, Thomas; Sevenheck, Christian
Non-affine Landau-Ginzburg models and intersection cohomology
EN
Ann. Sci. ??c. Norm. Sup??r. (4) 50, No. 3, 665-753 (2017).
00368633
2017
j
14J33 14M25 32S40 32S60 14D07 34Mxx 53D45
Gauss-Manin system; hypergeometric \(\mathcal{D}\)-module; toric variety; intersection cohomology; Radon transformation; Landau-Ginzburg model; Calabi-Yau hypersurface
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.
Vladimir P. Kostov (Nice)