Tetragonal curves, scrolls and $K3$ surfaces
نویسندگان
چکیده
منابع مشابه
Rational curves on K3 surfaces
This document is based on lectures given at the 2007 NATO Advanced Study Institute on ‘Higher-Dimensional Geometry over Finite Fields’, organized at the University of Göttingen by Yuri Tschinkel, and on lectures given at the 2010 summer school ‘Arithmetic Aspects of Rational Curves’, organized at the Institut Fourier in Grenoble by Emmanuel Peyre. This work is supported in part by National Scie...
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— We study the distribution of algebraic points on K3 surfaces.
متن کاملK3 Surfaces, Rational Curves, and Rational Points
We prove that for any of a wide class of elliptic surfaces X defined over a number field k, if there is an algebraic point on X that lies on only finitely many rational curves, then there is an algebraic point on X that lies on no rational curves. In particular, our theorem applies to a large class of elliptic K3 surfaces, which relates to a question posed by Bogomolov in 1981. Mathematics Subj...
متن کاملK3 Surfaces, Rational Curves, and Rational Points
We prove that for any of a wide class of elliptic surfaces X defined over a number field k, if there is an algebraic point on X that lies on only finitely many rational curves, then there is an algebraic point on X that lies on no rational curves. In particular, our theorem applies to a large class of elliptic K3 surfaces, which relates to a question posed by Bogomolov in 1981. Mathematics Subj...
متن کاملDensity of Rational Curves on K3 Surfaces
Using the dynamics of self rational maps of elliptic K3 surfaces together with deformation theory, we prove that the union of rational curves is dense on a very general K3 surface and that the union of elliptic curves is dense in the 1st jet space of a very general K3 surface, both in the strong topology. The techniques developed here also lend themselves to applications to Abel-Jacobi images, ...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1997
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-97-01811-4