Global matrix factorizations

Details Global matrix factorizations Global matrix factorizations

2011-01-31

arxiv.org/abs/1101.5847v1

Mathematics

Algebraic Geometry

Scientific paper

We study matrix factorization and curved module categories for Landau-Ginzburg models (X,W) with X a smooth quasi-projective variety, extending parts of the work of Dyckerhoff for the case of affine X. We equip these categories with model category structures, extending the work of Positselski. Using results of Rouquier and Orlov, we obtain compact generators for our categories. Via To\"en's derived Morita theory, we identify Hochschild cohomology with derived endomorphisms of the diagonal curved module. We compute the latter and get the expected result. Finally, we show that our categories are smooth, proper when the singular locus of W is proper, and Calabi-Yau when X is Calabi-Yau.

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