A Diophantine problem on algebraic curves over function fields of positive characteristic
J.F. Voloch (1991)
Bulletin de la Société Mathématique de France
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J.F. Voloch (1991)
Bulletin de la Société Mathématique de France
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Lomont, Chris (2002)
Experimental Mathematics
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Carvalho, Cícero F. (1999)
International Journal of Mathematics and Mathematical Sciences
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Gerhard Frey (1986)
Compositio Mathematica
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Serge Lang (1960)
Publications Mathématiques de l'IHÉS
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Dimitrios Poulakis (2003)
Acta Arithmetica
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Emrah Çakçak, Ferruh Özbudak (2005)
Acta Arithmetica
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Dan Abramovich, Joe Harris (1991)
Compositio Mathematica
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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.
Monnier, Jean-Philippe (2003)
Advances in Geometry
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Marco Andreatta, Elena Chierici, Gianluca Occhetta (2004)
Open Mathematics
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Let X be a Fano variety of dimension n, pseudoindex i X and Picard number ρX. A generalization of a conjecture of Mukai says that ρX(i X−1)≤n. We prove that the conjecture holds for a variety X of pseudoindex i X≥n+3/3 if X admits an unsplit covering family of rational curves; we also prove that this condition is satisfied if ρX> and either X has a fiber type extremal contraction or has not small extremal contractions. Finally we prove that the conjecture holds if X has dimension...
M. R. Gonzalez-Dorrego (2006)
Annales Polonici Mathematici
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Let k be an algebraically closed field of characteristic 0. Let C be an irreducible nonsingular curve in ℙⁿ such that 3C = S ∩ F, where S is a hypersurface and F is a surface in ℙⁿ and F has rational triple points. We classify the rational triple points through which such a curve C can pass (Theorem 1.8), and give an example (1.12). We only consider reduced and irreducible surfaces.