Abstract
AbstractLetX⊂ ℙnbe an unramified real curve withX(ℝ) ≠ 0. Ifn≥ 3 is odd, Huisman [9] conjectured thatXis anM-curve and that every branch ofX(ℝ) is a pseudo-line. Ifn≥ 4 is even, he conjectures thatXis a rational normal curve or a twisted form of such a curve. Recently, a family of unramifiedM-curves in ℙ3providing counterexamples to the first conjecture was constructed in [11]. In this note we construct another family of counterexamples that are not evenM-curves. We remark that the second conjecture follows for generic curves of odd degree from the de Jonquières formula.
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