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A K3 Surface Associated With Certain Integral Matrices Having Integral Eigenvalues

Published online by Cambridge University Press:  20 November 2018

Ronald van Luijk
Affiliation:
Department of Mathematics, University of California, Berkeley, CA 94720-3840 e-mail: rmluijk@math.berkeley.edu
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Abstract

In this article we will show that there are infinitely many symmetric, integral 3 × 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 $\text{K3}$ surface are dense. We will also compute the entire Néron–Severi group of this surface and find all low degree curves on it.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2006

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