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1. CMB 2006 (vol 49 pp. 560)
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A K3 Surface Associated With Certain Integral Matrices Having Integral Eigenvalues 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 non-Kummer, singular
K3 surface
are dense. We will also compute the entire N\'eron--Severi group of
this surface and find all low degree curves on it.
Keywords:symmetric matrices, eigenvalues, elliptic surfaces, K3 surfaces, Néron--Severi group, rational curves, Diophantine equations, arithmetic geometry, algebraic geometry, number theory Categories:14G05, 14J28, 11D41 |