A K3 Surface Associated With Certain Integral Matrices Having Integral Eigenvalues

Canadian mathematical bulletin

关键词: symmetric matrices;    eigenvalues;    elliptic surfaces;    K3 surfaces;    Néron--Severi group;    rational curves;    Diophantine equations;    arithmetic geometry;    algebraic geometry;    number theory;   

DOI  :  10.4153/CMB-2006-053-6

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

In this article we will show that there are infinitely manysymmetric, integral $3 imes 3$ matrices, with zeros on thediagonal, whose eigenvalues are all integral. We will do this byproving that the rational points on a certain non-Kummer, singularK3 surfaceare dense. We will also compute the entire Néron-Severi group ofthis surface and find all low degree curves on it.

【 授权许可】

Unknown