Classification of holomorphic vector bundles on noncommutative two-tori

Abstract

We prove that every holomorphic vector bundle on a noncommutative two-torus $T$ can be obtained by successive extensions from standard holomorphic bundles considered in math.QA/0211262. This implies that the category of holomorphic bundles on $T$ is equivalent to the heart of certain $t$-structure on the derived category of coherent sheaves on an elliptic curve.

AMSLatex, 18 pages

References in corpus (1)

• Categories of holomorphic vector bundles on noncommutative two-tori

Cited by in corpus (13)

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• Lecture Notes on Noncommutative Algebraic Geometry and Noncommutative Tori
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• Some remarks on mirror symmmetry and noncommutative elliptic curves
• On some approaches towards non-commutative algebraic geometry
• Kähler structure on certain $C^{\ast }$-dynamical systems and the noncommutative even dimensional tori
• Morphisms to noncommutative projective lines