Contents Online
Mathematical Research Letters
Volume 20 (2013)
Number 1
Global matrix factorizations
Pages: 91 – 106
DOI: https://dx.doi.org/10.4310/MRL.2013.v20.n1.a9
Authors
Abstract
We study matrix factorization and curved module categories for Landau–Ginzburg models $(X,W)$ with $X$ a smooth variety, extending parts of the work of Dyckerhoff. Following Positselski, we equip these categories with model category structures. Using results of Rouquier and Orlov, we identify compact generators. Via Toën’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 the total space $X$ is Calabi–Yau.
Published 20 September 2013