M-curves of degree 9 with deep nests

June 2009
Journal of the London Mathematical Society;Jun2009, Vol. 79 Issue 3, p649
Academic Journal
The first part of Hilberts 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.


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