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Annales scientifiques de l'ENS - Parutions - série 4, 50 (2017)

Parutions < série 4, 50

ANNALES SCIENTIFIQUES DE L’ÉCOLE NORMALE SUPÉRIEURE, série 4 50, fascicule 3 (2017)

Thomas Reichelt, Christian Sevenheck
Non-affine Landau-Ginzburg models and intersection cohomology
Annales scientifiques de l'ENS 50, fascicule 3 (2017), 665-753

Télécharger cet article : Fichier PDF

Résumé :
Modèles de Landau-Ginzburg non affines et cohomologie d'intersection
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.

Mots-clefs : Systèmes de Gauß-Manin, D-module hypergéométrique, variété torique, cohomologie d'intersection, transformation de Radon

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.

Keywords: Gauß-Manin system, hypergeometric D-module, toric variety, intersection cohomology, Radon transformation

Class. math. : 14J33, 14M25, 32S40, 32S60, 14D07, 34Mxx, 53D45


ISSN : 0012-9593
Publié avec le concours de : Centre National de la Recherche Scientifique

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