Affine varieties with stably trivial algebraic vector bundles
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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.References
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Additional Information
- Zbigniew Jelonek
- Affiliation: Instytut Matematyczny, Polska Akademia Nauk, Śniadeckich 8, 00-956 Warszawa, Poland
- Email: najelone@cyf-kr.edu.pl
- 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
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 3105-3109
- MSC (2010): Primary 14R10
- DOI: https://doi.org/10.1090/S0002-9939-10-10401-8
- MathSciNet review: 2653935