Holomorphic bundles on 2-dimensional noncommutative toric orbifolds

2004/10/12 by Alexander Polishchuk, Polishchuk, Alexander · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #math.AG #math.QA

paper · pdf · doi:10.48550/arxiv.math/0410283

Latex, 19 pages, references added

openalex publication_date 2004/10/12 · arxiv created 2004/11/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 algebras Λ. As an application we finish the computation of K₀-groups of the crossed product algebras describing the above orbifolds initiated by Kumjian, Walters and Buck. Also, we describe a torsion pair in the category of Λ-modules, such that the tilting with respect to this torsion pair gives the category of holomorphic bundles on T_θ/G.

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