Potential Density of Rational Points for K3 Surfaces over Function Fields
نویسنده
چکیده
We give examples of non-isotrivial K3 surfaces over complex function fields with Zariski-dense rational points and NéronSeveri rank one.
منابع مشابه
K3 surfaces over number fields with geometric Picard number one
A long-standing question in the theory of rational points of algebraic surfaces is whether a K3 surface X over a number field K acquires a Zariski-dense set of L-rational points over some finite extension L/K. In this case, we say X has potential density of rational points. In case XC has Picard rank greater than 1, Bogomolov and Tschinkel [2] have shown in many cases that X has potential densi...
متن کاملPotential density of rational points on the variety of lines of a cubic fourfold
Recall that for a variety X defined over a field k, rational points are said to be potentially dense in X if for some finite extension k′ of k, X(k′) is Zariski dense in X. For example, this is the case if X is a rational or a unirational variety. If k is a number field, a conjecture of Lang and Vojta, proved in dimension 1 by Faltings, but still open even in dimension two, predicts that variet...
متن کاملA Computational Investigation of Wehler K3 Surfaces
This article examines dynamical systems on a class of K3 surfaces in P×P with an infinite automorphism group. In particular, this article develops an algorithm to find Q-rational periodic points using information over Fp for various primes p. This algorithm is then optimized to examine the growth of the average number of cycles versus p and to determine the number of Fpm -rational points. The p...
متن کاملOn an automorphism of Hilb of certain K3 surfaces
In a recent note [O], K. Oguiso uses the structure of the cohomology of compact hyperkähler manifolds ([V]) to describe the behaviour of the dynamical degrees of an automorphism of such a manifold, and makes an explicit computation in some particular cases. One of his examples is the following: he considers a K3 surface S admitting two embeddings as a quartic in P (given by two different very a...
متن کاملThe Topology of Rational Points
Introduction 1. Comparison of Density Conditions 2. Curves 3. Conic Bundles over P 4. Smooth Cubic Hypersurfaces 5. Smooth Complete Intersections of Two Quadrics in P 6. Elliptic Surfaces 7. Some Abelian Varieties 8. Some Kummer Surfaces 9. Some Other K3 Surface Examples References The aim of this article is to provoke a discussion concerning the general nature of the topological closure of the...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005