A real algebraic vector bundle is strongly algebraic whenever its total space is affine. (English) Zbl 0868.14009
Akbulut, Selman (ed.), Real algebraic geometry and topology. A conference on real algebraic geometry and topology, December 17-21, 1993, Michigan State University, East Lansing, MI, USA. Providence, RI: American Mathematical Society. Contemp. Math. 182, 117-119 (1995); correction ibid. 253, 179 (2000).
Summary: The aim of this note is to prove the following statement. Let \(X\) be an affine real algebraic variety and let \(\xi= (E,\pi)\) be a real algebraic vector bundle over \(X\). Then, \(\xi\) is strongly algebraic if and only if \(E\) is an affine real algebraic variety.
For the entire collection see [Zbl 0814.00016].
For the entire collection see [Zbl 0814.00016].
MSC:
| 14F05 | Sheaves, derived categories of sheaves, etc. (MSC2010) |
| 14P05 | Real algebraic sets |
