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M-curves of degree 9 with deep nests

Séverine Fiedler-Le Touzé
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Abstract

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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Séverine Fiedler-Le Touzé. 2008-10-10. M-curves of degree 9 with deep nests. https://doi.org/10.1112/jlms%2Fjdp010

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