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On a desingularization of the moduli space of noncommutative tori

Authors:	Igor Nikolaev

Institution:	The Fields Institute for Mathematical Sciences, Toronto, Ontario, Canada

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.

Keywords:	Complex tori noncommutative tori

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