M ‐curves of degree 9 with deep nests

DOI10.1112/JLMS/JDP010zbMATH Open1163.14032arXivmath/0610792OpenAlexW2122210553MaRDI QIDQ3630823

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Publication date: 4 June 2009

Published in: (Search for Journal in Brave)

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 $mgeq8$, 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.

Full work available at URL: https://arxiv.org/abs/math/0610792

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