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Journal of the London Mathematical Society Advance Access published online on March 27, 2009
Journal of the London Mathematical Society, doi:10.1112/jlms/jdp010
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© 2009 London Mathematical Society

M-curves of degree 9 with deep nests

Séverine Fiedler-Le Touzé

Institut de Mathématiques de Toulouse
Université Paul Sabatier
118 route de Narbonne
31062 Toulouse cedex 9
France

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.

2000 Mathematics Subject Classification 14P25 (primary), 14Q05 (secondary).

Received March 10, 2008; revised December 17, 2008;
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