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Holomorphic bundles on 2-dimensional noncommutative toric orbifolds

  • A. Polishchuk
Part of the Aspects of Mathematics book series (ASMA)

Abstract

We define the notion of a holomorphic bundle on the noncommutative toric orbifold T θ/G associated with an action of a finite cyclic group G on an irrational rotation algebra. We prove that the category of such holomorphic bundles is abelian and its derived category is equivalent to the derived category of modules over a finite-dimensional algebra ∧. As an application we finish the computation of K 0-groups of the crossed product algebras describing the above orbifolds initiated in [18], [29], [30], [12] and [13]. Also, we describe a torsion pair in the category of ∧-modules, such that the tilting with respect to this torsion pair gives the category of holomorphic bundles on T θ/G.

Keywords

Vector Bundle Elliptic Curve Full Subcategory Coherent Sheave Galois Covering 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Friedr. Vieweg & Sohn Verlag ∣ GWV Fachverlage GmbH, Wiesbaden 2006

Authors and Affiliations

  • A. Polishchuk

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