  Seiberg-Witten maps are a well-established method to locally construct
noncommutative gauge theories starting from commutative gauge theories. We
revisit and classify the ambiguities and the freedom in the definition.
  Geometrically, Seiberg-Witten maps provide a quantization of bundles with
connections. We study the case of U(n)-vector bundles on two-dimensional tori,
prove the existence of globally defined Seiberg-Witten maps (induced from the
plane to the torus) and show their compatibility with Morita equivalence.
