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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.

##### MSC:
 14H45 Special algebraic curves and curves of low genus 14P25 Topology of real algebraic varieties 14N05 Projective techniques in algebraic geometry
##### Keywords:
Hilbert 16-th problem; arrangement