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M ‐curves of degree 9 with deep nests
Author(s) -
Fiedler-Le Touzé Séverine
Publication year - 2009
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdp010
Subject(s) - isotopy , degree (music) , nest (protein structural motif) , plane curve , mathematics , plane (geometry) , artificial intelligence , geometry , pure mathematics , computer science , physics , nuclear magnetic resonance , acoustics
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 ⩾ 8, one restricts the study to the case of 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 exclude ten isotopy types with a deep nest and no outer ovals.