Matrix factorizations and singularity categories for stacks

[Factorisations matricielles et catégories des singularités pour les champs algébriques]

Polishchuk, Alexander ; Vaintrob, Arkady

Annales de l'Institut Fourier, Tome 61 (2011), p. 2609-2642 / Harvested from Numdam

Résumé

On étudie les factorisations matricielles d’un potentiel W qui est une section d’un fibré en droites sur un champ algébrique. On établit une relation entre la catégorie dérivée correspondante (la catégorie des D-branes de type B dans le modèle de Landau-Ginzburg avec potentiel W) et la catégorie des singularités du lieu des zéros de W généralisant un théorème d’Orlov. On utilise ce résultat pour construire des foncteurs image directe pour les factorisations matricielles à supports relativement propres.

Abstract

We study matrix factorizations of a potential W which is a section of a line bundle on an algebraic stack. We relate the corresponding derived category (the category of D-branes of type B in the Landau-Ginzburg model with potential W) with the singularity category of the zero locus of W generalizing a theorem of Orlov. We use this result to construct push-forward functors for matrix factorizations with relatively proper support.

Détail

Publié le : 2011-01-01

MR 3112502 | Zbl 1278.13014

DOI : https://doi.org/10.5802/aif.2788
Classification:  14A20,  14J17,  18E30
Mots clés: factorisations matricielles, catégorie des singularités, champ algébrique

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