Abstract view
A K3 Surface Associated With Certain Integral Matrices Having Integral Eigenvalues


Published:20061201
Printed: Dec 2006
Abstract
In this article we will show that there are infinitely many
symmetric, integral $3 \times 3$ matrices, with zeros on the
diagonal, whose eigenvalues are all integral. We will do this by
proving that the rational points on a certain nonKummer, singular
K3 surface
are dense. We will also compute the entire NéronSeveri group of
this surface and find all low degree curves on it.
Keywords: 
symmetric matrices, eigenvalues, elliptic surfaces, K3 surfaces, NéronSeveri group, rational curves, Diophantine equations, arithmetic geometry, algebraic geometry, number theory
symmetric matrices, eigenvalues, elliptic surfaces, K3 surfaces, NéronSeveri group, rational curves, Diophantine equations, arithmetic geometry, algebraic geometry, number theory
