On Huisman’s conjectures about unramified real curves
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Mario Kummer
Abstract
Let X ⊂ ℙn be an unramified real curve with X(ℝ) ≠ 0. If n ≥ 3 is odd, Huisman [9] conjectured that X is an M-curve and that every branch of X(ℝ) is a pseudo-line. If n ≥ 4 is even, he conjectures that X is a rational normal curve or a twisted form of such a curve. Recently, a family of unramified M-curves in ℙ3 providing counterexamples to the first conjecture was constructed in [11]. In this note we construct another family of counterexamples that are not even M-curves. We remark that the second conjecture follows for generic curves of odd degree from the de Jonquières formula.
Communicated by: C. Scheiderer
Acknowledgements
We would like to thank Daniel Plaumann for the very helpful discussions that initiated this project.
References
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Articles in the same Issue
- Frontmatter
- An 𝔽p2-maximal Wiman sextic and its automorphisms
- Pseudo-algebraic Ricci solitons on Einstein nilradicals
- The wobbly divisors of the moduli space of rank-2 vector bundles
- Symmetries of complex analytic vector fields with an essential singularity on the Riemann sphere
- Betti numbers and pseudoeffective cones in 2-Fano varieties
- The generating rank of a polar Grassmannian
- The Beckman–Quarles theorem via the triangle inequality
- On Huisman’s conjectures about unramified real curves
- Geodesic orbit Finsler spaces with K ≥ 0 and the (FP) condition
- On the Segre invariant for rank two vector bundles on ℙ2
- Lifting coarse homotopies
- How to construct all metric f-K-contact manifolds
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Articles in the same Issue
- Frontmatter
- An 𝔽p2-maximal Wiman sextic and its automorphisms
- Pseudo-algebraic Ricci solitons on Einstein nilradicals
- The wobbly divisors of the moduli space of rank-2 vector bundles
- Symmetries of complex analytic vector fields with an essential singularity on the Riemann sphere
- Betti numbers and pseudoeffective cones in 2-Fano varieties
- The generating rank of a polar Grassmannian
- The Beckman–Quarles theorem via the triangle inequality
- On Huisman’s conjectures about unramified real curves
- Geodesic orbit Finsler spaces with K ≥ 0 and the (FP) condition
- On the Segre invariant for rank two vector bundles on ℙ2
- Lifting coarse homotopies
- How to construct all metric f-K-contact manifolds
- An extremum problem for the power moment of a convex polygon contained in a disc
- Sharply transitive sets in PGL2(K)
