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Affine varieties with stably trivial algebraic vector bundles

Author: Zbigniew Jelonek
Journal: Proc. Amer. Math. Soc. 138 (2010), 3105-3109
MSC (2010): Primary 14R10
Published electronically: April 29, 2010
MathSciNet review: 2653935
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Abstract: Let $ k$ be an algebraically closed field. For every affine variety $ X$ with dim $ X\ge 7$ we construct a smooth affine variety $ Y$ which is birationally equivalent to $ X$ and which possesses a stably trivial but not trivial algebraic vector bundle. We give some application of this fact to the cancellation problem.

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Zbigniew Jelonek
Affiliation: Instytut Matematyczny, Polska Akademia Nauk, Śniadeckich 8, 00-956 Warszawa, Poland

Keywords: Algebraic vector bundle, cancellation problem
Received by editor(s): December 15, 2008
Received by editor(s) in revised form: August 21, 2009, and December 9, 2009
Published electronically: April 29, 2010
Additional Notes: The author was partially supported by a grant from the Polish Ministry of Science, 2010-2013
Communicated by: Ted Chinburg
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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