Complex geometry of the noncommutative pillow

Tomasz Brzezinski (Swansea)

Frank Adams 1,

The classical pillow manifold obtained as a quotient of a non-free cyclic group action on the two-torus is an example of an orbifold. We describe a differential calculus and a complex structure on the non-commutative version of the classical pillow manifold, obtained by a cyclic group action on the non-commutative torus and reveal the surprising fact that this deformation of an orbifold has all the features of a smooth complex (non-commutative) curve.

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