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Propriétés arithmétiques d'une famille de surfaces K3

Published online by Cambridge University Press:  04 December 2007

HERVÉ BILLARD
HERVÉ BILLARD
Affiliation:
Université Paris 7, U.F.R. de Mathématiques, 2 Place Jussieu, 75251 Paris Cedex 05, France; e-mail: billard@mathp7.jussieu.fr
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Abstract

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We study a family of K3 surfaces which have a big automorphism group. We begin with generalisations of Silverman's results: construction of canonical heights, density of rational points in one orbit,… We continue the study in estimating the density of rational points on the orbiting rational curves; this estimate is compatible with Batyrev–Manin conjecture. Moreover we settle, under more geometric hypothesis, the number of rational points of such surfaces of bounded height.

Keywords

Surface K3orbitehauteur
Type
Research Article
Information
Compositio Mathematica , Volume 108 , Issue 3 , September 1997 , pp. 247 - 275
Copyright
© 1997 Kluwer Academic Publishers