Construction of real hypersurfaces [after Viro]. (Construction d’hypersurfaces réelles [d’après Viro].) (French) Zbl 0824.14045

Séminaire Bourbaki. Volume 1992/93. Exposés 760-774. Paris: Société Mathématique de France, Astérisque. 216, 69-86 (Exp. No. 763) (1993).
This is given an outline of the main ideas of Viro’s method of constructing real algebraic hypersurfaces [O. Ya. Viro in: Topology, general and algebraic topology, and applications, Proc. int. Conf., Leningrad 1982, Lect. Notes Math. 1060, 187-200 (1984; Zbl 0576.14031)], which led to a significant progress in Hilbert’s 16th problem. The method is demonstrated in the case of plane curves. Several generalizations of the method are discussed as well.
For the entire collection see [Zbl 0782.00042].


14P25 Topology of real algebraic varieties
14P05 Real algebraic sets
14J70 Hypersurfaces and algebraic geometry


Zbl 0576.14031
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