A K3 Surface Associated With Certain Integral Matrices Having Integral Eigenvalues

Luijk, Ronald van

Canadian mathematical bulletin, Tome 49 (2006) no. 4, pp. 560-577

Résumé

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.

Détail

DOI : 10.4153/CMB-2006-053-6

Mots-clés : 14G05, 14J28, 11D41, symmetric matrices, eigenvalues, elliptic surfaces, K3 surfaces, Néron–Severi group, rational curves, Diophantine equations, arithmetic geometry, algebraic geometry, number theory

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