  It is shown that the moduli space of the noncommutative tori A admits a
natural desingularization by the group Ext (A, A). Namely, we prove that the
moduli space of pairs (A, Ext (A,A)) is homeomorphic to a punctured
two-dimensional sphere. The proof is based on a correspondence (a covariant
functor) between the complex and noncommutative tori.

Operator Algebras;Algebraic Geometry