Cuspidal Projections of Space Curves.
Ragni Piene (1981)
Mathematische Annalen
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Displaying similar documents to “The degree of rational cuspidal curves.”
Cuspidal Projections of Space Curves.
Rational 1- and 2-cuspidal plane curves.
Fenske, Torsten (1999)
Beiträge zur Algebra und Geometrie
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On the method of Coleman and Chabauty.
William G. McCallum (1994)
Mathematische Annalen
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Pencils of irreducible rational curves and plane Jacobian conjecture
Nguyen Van Chau (2011)
Annales Polonici Mathematici
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In certain cases the invertibility of a polynomial map F = (P,Q): ℂ²→ ℂ² can be characterized by the irreducibility and the rationality of the curves aP+bQ = 0, (a:b) ∈ ℙ¹.
A Note on the Rational Cuspidal Curves
Piotr Nayar, Barbara Pilat (2014)
Bulletin of the Polish Academy of Sciences. Mathematics
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In this short note we give an elementary combinatorial argument, showing that the conjecture of J. Fernández de Bobadilla, I. Luengo-Velasco, A. Melle-Hernández and A. Némethi [Proc. London Math. Soc. 92 (2006), 99-138, Conjecture 1] follows from Theorem 5.4 of Brodzik and Livingston [arXiv:1304.1062] in the case of rational cuspidal curves with two critical points.
The Hodge Conjecture for Fourfolds Admitting a Covering by Rational Curves.
A. Conte, J.P. Murre (1978)
Mathematische Annalen
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On a class of rational cuspidal plane curves.
Hubert Flenner, Mikhail Zaidenberg (1996)
Manuscripta mathematica
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Trivial points on towers of curves
Xavier Xarles (2013)
Journal de Théorie des Nombres de Bordeaux
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In order to study the behavior of the points in a tower of curves, we introduce and study trivial points on towers of curves, and we discuss their finiteness over number fields. We relate the problem of proving that the only rational points are the trivial ones at some level of the tower, to the unboundeness of the gonality of the curves in the tower, which we show under some hypothesis.
Divisors on general curves and cuspidal rational curves.
D. Eisenbud, J. Harris (1983)
Inventiones mathematicae
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Local geometry of smooth curves passing through rational double points.
David B. Jaffe (1992)
Mathematische Annalen
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Appendix to "Plücker conditions on plane rational curves": Families of rational plane curves.
Stein Arild Stromme (1984)
Mathematica Scandinavica
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Rational Bézier curves with infinitely many integral points
Petroula Dospra (2023)
Archivum Mathematicum
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In this paper we consider rational Bézier curves with control points having rational coordinates and rational weights, and we give necessary and sufficient conditions for such a curve to have infinitely many points with integer coefficients. Furthermore, we give algorithms for the construction of these curves and the computation of theirs points with integer coefficients.