An application of ample vector bundles in real algebraic geometry
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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 $X$.References
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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
- Received by editor(s): February 5, 2010
- Published electronically: November 17, 2010
- Communicated by: Lev Borisov
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 1155-1161
- MSC (2010): Primary 14F05, 14F25, 14P05, 14P25
- DOI: https://doi.org/10.1090/S0002-9939-2010-10765-7
- MathSciNet review: 2748410