Rational points on K3 surfaces in ?1 � ?1 � ?1

1996 ◽  
Vol 305 (1) ◽  
pp. 541-558 ◽  
Author(s):  
A. Baragar
Keyword(s):  
K3 Surfaces ◽  
Rational Points

scholarly journals K3 surfaces, rational curves, and rational points

2010 ◽  
Vol 130 (7) ◽  
pp. 1470-1479 ◽  
Author(s):  
Arthur Baragar ◽  
David McKinnon
Keyword(s):  
K3 Surfaces ◽  
Rational Points ◽  
Rational Curves

scholarly journals Density of rational points on elliptic K3 surfaces

2000 ◽  
Vol 4 (2) ◽  
pp. 351-368 ◽  
Author(s):  
F. A. Bogomolov ◽  
Yu. Tschinkel
Keyword(s):  
K3 Surfaces ◽  
Rational Points

scholarly journals Non-Euclidean pythagorean triples, a problem of euler, and rational points on K3 surfaces

2008 ◽  
Vol 30 (4) ◽  
pp. 4-10 ◽  
Author(s):  
Robin Hartshorne ◽  
Ronald Van Luijk
Keyword(s):  
K3 Surfaces ◽  
Rational Points ◽  
Pythagorean Triples

scholarly journals Rational Points on Twisted K3 Surfaces and Derived Equivalences

2017 ◽  
pp. 13-28 ◽  
Author(s):  
Kenneth Ascher ◽  
Krishna Dasaratha ◽  
Alexander Perry ◽  
Rong Zhou
Keyword(s):  
K3 Surfaces ◽  
Rational Points ◽  
Derived Equivalences

scholarly journals Rational points on elliptic K3 surfaces of quadratic twist type

2020 ◽  
Author(s):  
Zhizhong Huang
Keyword(s):  
Elliptic Curves ◽  
K3 Surfaces ◽  
Rational Points ◽  
Zariski Topology ◽  
Quadratic Twists ◽  
Quadratic Twist ◽  
Quartic Polynomials

Abstract In studying rational points on elliptic K3 surfaces of the form $$\begin{equation*} f(t)y^2=g(x), \end{equation*}$$ where f, g are cubic or quartic polynomials (without repeated roots), we introduce a condition on the quadratic twists of two elliptic curves having simultaneously positive Mordell–Weil rank, and we relate it to the Hilbert property. Applying to surfaces of Cassels–Schinzel type, we prove unconditionally that rational points are dense both in Zariski topology and in real topology.

scholarly journals On an automorphism of Hilb[2] of certain K3 surfaces

2011 ◽  
Vol 54 (1) ◽  
pp. 1-7 ◽  
Author(s):  
Ekaterina Amerik
Keyword(s):  
Hilbert Scheme ◽  
K3 Surfaces ◽  
Rational Points ◽  
Potential Density ◽  
Punctual Hilbert Scheme

AbstractFollowing some remarks made by O'Grady and Oguiso, the potential density of rational points on the second punctual Hilbert scheme of certain K3 surfaces is proved.

Rational points on K3 surfaces: A new canonical height

1991 ◽  
Vol 105 (1) ◽  
pp. 347-373 ◽  
Author(s):  
Joseph H. Silverman
Keyword(s):  
K3 Surfaces ◽  
Rational Points ◽  
Canonical Height

scholarly journals Potential density of rational points for K3 surfaces over function fields

2008 ◽  
Vol 130 (5) ◽  
pp. 1263-1278
Author(s):  
Brendan Hassett ◽  
Yuri Tschinkel
Keyword(s):  
Function Fields ◽  
K3 Surfaces ◽  
Rational Points ◽  
Potential Density
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