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

 

An application of ample vector bundles in real algebraic geometry


Authors: Wojciech Kucharz and Kamil Rusek
Journal: Proc. Amer. Math. Soc. 139 (2011), 1155-1161
MSC (2010): Primary 14F05, 14F25, 14P05, 14P25
Published electronically: November 17, 2010
MathSciNet review: 2748410
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Abstract: Let $ E$ be an algebraic vector bundle on a compact nonsingular real algebraic set $ X$, and let $ Z$ be the zero locus of a ``generic'' algebraic section of $ E$. We investigate how certain cohomological invariants of $ X$ and $ Z$ are related. A crucial role in the proof is played by ample vector bundles on a suitable complexification of $ X$.


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Additional Information

Wojciech Kucharz
Affiliation: Institute of Mathematics, Jagiellonian University, ul. Profesora Łojasiewicza 6, 30-348 Kraków, Poland
Email: Wojciech.Kucharz@im.uj.edu.pl

Kamil Rusek
Affiliation: Institute of Mathematics, Jagiellonian University, ul. Profesora Łojasiewicza 6, 30-348 Kraków, Poland
Email: Kamil.Rusek@im.uj.edu.pl

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10765-7
PII: S 0002-9939(2010)10765-7
Keywords: Real algebraic set, algebraic vector bundle, algebraic cohomology class, nonsingular projective complexification, ample vector bundle
Received by editor(s): February 5, 2010
Published electronically: November 17, 2010
Communicated by: Lev Borisov
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.