Categories of holomorphic line bundles on higher dimensional noncommutative complex tori

Details Categories of holomorphic line bundles on higher dimensional noncommutative complex tori Categories of holomorphic line bundles on higher dimensional noncommutative complex tori

2005-10-14

arxiv.org/abs/hep-th/0510119v1

J.Math.Phys.48:053517,2007

Physics

High Energy Physics

High Energy Physics - Theory

28 pages

Scientific paper

10.1063/1.2719564

We construct explicitly noncommutative deformations of categories of holomorphic line bundles over higher dimensional tori. Our basic tools are Heisenberg modules over noncommutative tori and complex/holomorphic structures on them introduced by A. Schwarz. We obtain differential graded (DG) categories as full subcategories of curved DG categories of Heisenberg modules over the complex noncommutative tori. Also, we present the explicit composition formula of morphisms, which in fact depends on the noncommutativity.

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