On a desingularization of the moduli space of noncommutative tori

Abstract:

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