Non-affine Landau-Ginzburg models  and intersection cohomology

Reichelt, Thomas; Sevenheck, Christian

doi:10.24033/asens.2330

Non-affine Landau-Ginzburg models and intersection cohomology
[Modèles de Landau-Ginzburg non affines et cohomologie d'intersection]

Reichelt, Thomas ; Sevenheck, Christian

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 50 (2017) no. 3, pp. 665-753.

Résumé
Abstract

Nous construisons un modèle de Landau-Ginzburg pour les intersections complètes numériquement effectives dans les variétés toriques lisses. Il s'agit de compactifications partielles de familles de polynômes de Laurent. Nous démontrons un théorème de symétrie miroir qui exprime le $𝒟$ -module quantique de la partie ambiante de la cohomologie de la sous-variété comme un $𝒟$ -module de cohomologie d'intersection défini par cette compactification partielle. Nous en déduisons des propriétés de Hodge de ces systèmes différentiels.

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.

Publié le : 2017-11-12

DOI : 10.24033/asens.2330

Classification : 14J33, 14M25, 32S40, 32S60, 14D07, 34Mxx, 53D45
Keywords: Gauß-Manin system, hypergeometric $\mathcal {D}$-module, toric variety, intersection cohomology, Radon transformation
Mot clés : Systèmes de Gauß-Manin, $\mathcal {D}$-module hypergéométrique, variété torique, cohomologie d'intersection, transformation de Radon

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     title = {Non-affine {Landau-Ginzburg} models  and intersection cohomology},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {665--753},
     publisher = {Soci\'et\'e Math\'ematique de France. Tous droits r\'eserv\'es},
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}

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Reichelt, Thomas; Sevenheck, Christian. Non-affine Landau-Ginzburg models  and intersection cohomology. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 50 (2017) no. 3, pp. 665-753. doi : 10.24033/asens.2330. http://www.numdam.org/articles/10.24033/asens.2330/

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