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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On a desingularization of the moduli space of noncommutative tori


Author: Igor Nikolaev
Journal: Proc. Amer. Math. Soc. 136 (2008), 3769-3774
MSC (2000): Primary 14H52, 46L85
Published electronically: June 24, 2008
MathSciNet review: 2425714
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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.


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Additional Information

Igor Nikolaev
Affiliation: The Fields Institute for Mathematical Sciences, Toronto, Ontario, Canada
Email: igor.v.nikolaev@gmail.com

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09465-3
PII: S 0002-9939(08)09465-3
Keywords: Complex tori, noncommutative tori
Received by editor(s): March 30, 2007
Received by editor(s) in revised form: September 6, 2007
Published electronically: June 24, 2008
Additional Notes: The author was partially supported by NSERC
Communicated by: Marius Junge
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.