Classification of holomorphic vector bundles on noncommutative two-tori

By Alexander Polishchuk. Documenta Mathematica, 2003

59 citations recorded by the source corpus.

We prove that every holomorphic vector bundle on a noncommutative two-torus T can be obtained by successive exten- sions from standard holomorphic bundles considered in (2). This im- plies that the category of holomorphic bundles on T is equivalent to the heart of a certain t-structure on the derived category of coherent sheaves on an elliptic curve.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/392118f431d1f30bf427021bbe55a0c8d0c48007

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In Geometry and Topology

1. Yuri I. Manin
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In Mathematical Physics

1. Yuri I. Manin
2. Brendan Hassett
3. R. Hain

Citations in the corpus

• The notion of dimension in geometry and algebra (2005, methodology): “Holomorphic maps between modules are maps commuting with ∇. Similar definitions can be stated for left modules (see [Co1], [PoS], [Po1], [ Po2 ]).”