A K3 surface associated to certain integral matrices with integral eigenvalues

Details A K3 surface associated to certain integral matrices with integral eigenvalues A K3 surface associated to certain integral matrices with integral eigenvalues

2004-11-26

arxiv.org/abs/math/0411600v2

Mathematics

Algebraic Geometry

21 pages, Latex. Changed some typos, definition 5.5, part of the proof of proposition 6.1, and added a reference. Submitted a

Scientific paper

In this article we will show that there are infinitely many symmetric,
integral 3 x 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
Neron-Severi group of this surface and find all low degree curves on it.

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