On -maximal curves of genus .
Abdón, Miriam, Torres, Fernando (2005)
Beiträge zur Algebra und Geometrie
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Displaying similar documents to “Siegel’s theorem and the Shafarevich conjecture”
On -maximal curves of genus .
Linearly Normal Curves in P^n
Pasarescu, Ovidiu (2004)
Serdica Mathematical Journal
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2000 Mathematics Subject Classification: 14H45, 14H50, 14J26. We construct linearly normal curves covering a big range from P^n, n ≥ 6 (Theorems 1.7, 1.9). The problem of existence of such algebraic curves in P^3 has been solved in [4], and extended to P^4 and P^5 in [10]. In both these papers is used the idea appearing in [4] and consisting in adding hyperplane sections to the curves constructed in [6] (for P^3) and [15, 11] (for P^4 and P^5) on some special surfaces. In...
Higher genus abelian functions associated with cyclic trigonal curves.
England, Matthew (2010)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Variations on a theme of Runge: effective determination of integral points on certain varieties
Aaron Levin (2008)
Journal de Théorie des Nombres de Bordeaux
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We consider some variations on the classical method of Runge for effectively determining integral points on certain curves. We first prove a version of Runge’s theorem valid for higher-dimensional varieties, generalizing a uniform version of Runge’s theorem due to Bombieri. We then take up the study of how Runge’s method may be expanded by taking advantage of certain coverings. We prove both a result for arbitrary curves and a more explicit result for superelliptic curves. As an application...
3-type curves in the Euclidean space E5
Miroslava Petrović-Torgašev (2002)
Kragujevac Journal of Mathematics
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Ideal class groups, Hilbert’s irreducibility theorem, and integral points of bounded degree on curves
Aaron Levin (2007)
Journal de Théorie des Nombres de Bordeaux
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We study the problem of constructing and enumerating, for any integers , number fields of degree whose ideal class groups have “large" -rank. Our technique relies fundamentally on Hilbert’s irreducibility theorem and results on integral points of bounded degree on curves.
The fluctuations in the number of points on a family of curves over a finite field
Maosheng Xiong (2010)
Journal de Théorie des Nombres de Bordeaux
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Let be a positive integer, a finite field of cardinality with . In this paper, inspired by [, , ] and using a slightly different method, we study the fluctuations in the number of -points on the curve given by the affine model , where is drawn at random uniformly from the set of all monic -th power-free polynomials of degree as . The method also enables us to study the fluctuations in the number of -points on the same family of curves arising from the set of monic...