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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Non-commutative $ \mathbb{P}^1$-bundles over commutative schemes

Author: M. Van den Bergh
Journal: Trans. Amer. Math. Soc. 364 (2012), 6279-6313
MSC (2010): Primary 18E15; Secondary 14D15
Published electronically: July 11, 2012
MathSciNet review: 2958936
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Abstract: In this paper we develop the theory of non-commutative $ \mathbb{P}^1$-bundles over commutative (smooth) schemes. Such non-commutative $ \mathbb{P}^1$-bundles occur in the theory of $ D$-modules but our definition is more general. We can show that every non-commutative deformation of a Hirzebruch surface is given by a non-commutative $ \mathbb{P}^1$-bundle over  $ \mathbb{P}^1$ in our sense.

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Additional Information

M. Van den Bergh
Affiliation: Department of Mathematics, Universiteit Hasselt, 3590 Diepenbeek, Belgium

PII: S 0002-9947(2012)05469-9
Keywords: Non-commutative geometry, Hirzebruch surfaces, deformations
Received by editor(s): February 15, 2010
Received by editor(s) in revised form: September 20, 2010
Published electronically: July 11, 2012
Additional Notes: The author is a senior researcher at the FWO
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.