Euclidean algorithm and Kummer covers with many points.
Garzón, Alvaro (2003)
Revista Colombiana de Matemáticas
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Displaying similar documents to “A Diophantine problem on algebraic curves over function fields of positive characteristic”
Euclidean algorithm and Kummer covers with many points.
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Serge Lang (1960)
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Descent via (3,3)-isogeny on Jacobians of genus 2 curves
Nils Bruin, E. Victor Flynn, Damiano Testa (2014)
Acta Arithmetica
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We give a parametrization of curves C of genus 2 with a maximal isotropic (ℤ/3)² in J[3], where J is the Jacobian variety of C, and develop the theory required to perform descent via (3,3)-isogeny. We apply this to several examples, where it is shown that non-reducible Jacobians have non-trivial 3-part of the Tate-Shafarevich group.
On the height constant for curves of genus two, II
Michael Stoll (2002)
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Gerhard Frey (1986)
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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.
On the existence of k-normal curves of given degree and genus in projective spaces.
Edoardo Ballico, N. Chiarli, S. Greco (2004)
Collectanea Mathematica
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We find some ranges for the 4-tuples of integers (d,g,n,r) for which there is a smooth connected non-degenerate curve of degree d and genus g, which is k-normal for every k ≤ r.
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.