M-curves of degree 9 with deep nests

Details M-curves of degree 9 with deep nests M-curves of degree 9 with deep nests

2006-10-26

arxiv.org/abs/math/0610792v4

Mathematics

Algebraic Geometry

16 pages, 11 figures v.4 minimal corrections

Scientific paper

The first part of Hilbert's sixteenth problem deals with the classification of the isotopy types realizable by real plane algebraic curves of given degree $m$. For $m \geq 8$, one restricts the study to the case of the $M$-curves. For $m=9$, the classification is still wide open. We say that an $M$-curve of degree 9 has a deep nest if it has a nest of depth 3. In the present paper, we prohibit 10 isotopy types with deep nests and no outer ovals.

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