Rational 1- and 2-cuspidal plane curves.
Fenske, Torsten (1999)
Beiträge zur Algebra und Geometrie
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Fenske, Torsten (1999)
Beiträge zur Algebra und Geometrie
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Stein Arild Stromme (1984)
Mathematica Scandinavica
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Dimitrios Poulakis (2003)
Acta Arithmetica
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Matt DeLong (2002)
Acta Arithmetica
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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.
Hubert Flenner, Mikhail Zaidenberg (1996)
Manuscripta mathematica
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Fumio Sakai, Takashi Matsuoka (1989)
Mathematische Annalen
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Arnaldo Garcia, Luciane Quoos (2001)
Acta Arithmetica
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D. Eisenbud, J. Harris (1983)
Inventiones mathematicae
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Xian Wu (1994)
Manuscripta mathematica
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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.
Maciej Ulas (2010)
Acta Arithmetica
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Alexandre Eremenko (2012)
Fundamenta Mathematicae
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Jordan analytic curves which are invariant under rational functions are studied.
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.
Petulante, Nelson, Kaja, Ifeoma (2000)
International Journal of Mathematics and Mathematical Sciences
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J. Achari (1979)
Publications de l'Institut Mathématique
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Galbraith, Steven D. (1999)
Experimental Mathematics
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