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On the classification of decomposing plane algebraic curves. (English) Zbl 0789.14028
Real algebraic geometry, Proc. Conf., Rennes/Fr. 1991, Lect. Notes Math. 1524, 52-74 (1992).
[For the entire collection see Zbl 0756.00007.]
This report represents a survey of results on the arrangement of curves which are decomposed into product of curves “in general position” in real projective plane \(\mathbb{R}\mathbb{P}^ 2\). The problem under consideration is in close connection with the classical question of the Hilbert 16-th problem on the topology and arrangement of nonsingular algebraic varieties. Note that in some cases we receive, in fact, the classification of the nonsingular affine plane algebraic curves.

14H45 Special algebraic curves and curves of low genus
14P25 Topology of real algebraic varieties
14N05 Projective techniques in algebraic geometry