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M-curves of degree 9 or 11 with one unique non-empty oval

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Preprint
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Submission Date
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arXiv ID: 1412.5313
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arXiv
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Abstract

In this note, we consider M-curves of odd degree with real scheme of the form $< \mathcal{J} \amalg \alpha \amalg 1 < \beta > >$. With help of complex orientations, we prove that for $m = 9$, $\alpha \geq 2$, and for $m = 11$, $\alpha \geq 3$.

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