A K3 Surface Associated With Certain Integral Matrices Having Integral Eigenvalues
Canadian mathematical bulletin, Tome 49 (2006) no. 4, pp. 560-577
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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.
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
Luijk, Ronald van. A K3 Surface Associated With Certain Integral Matrices Having Integral Eigenvalues. Canadian mathematical bulletin, Tome 49 (2006) no. 4, pp. 560-577. doi: 10.4153/CMB-2006-053-6
@article{10_4153_CMB_2006_053_6,
author = {Luijk, Ronald van},
title = {A {K3} {Surface} {Associated} {With} {Certain} {Integral} {Matrices} {Having} {Integral} {Eigenvalues}},
journal = {Canadian mathematical bulletin},
pages = {560--577},
year = {2006},
volume = {49},
number = {4},
doi = {10.4153/CMB-2006-053-6},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2006-053-6/}
}
TY - JOUR AU - Luijk, Ronald van TI - A K3 Surface Associated With Certain Integral Matrices Having Integral Eigenvalues JO - Canadian mathematical bulletin PY - 2006 SP - 560 EP - 577 VL - 49 IS - 4 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2006-053-6/ DO - 10.4153/CMB-2006-053-6 ID - 10_4153_CMB_2006_053_6 ER -
%0 Journal Article %A Luijk, Ronald van %T A K3 Surface Associated With Certain Integral Matrices Having Integral Eigenvalues %J Canadian mathematical bulletin %D 2006 %P 560-577 %V 49 %N 4 %U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2006-053-6/ %R 10.4153/CMB-2006-053-6 %F 10_4153_CMB_2006_053_6
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