Transcendental lattices and supersingular reduction lattices of a singular $K3$ surface
| dc.creator | Shimada, Ichiro | |
| dc.date | 2006-11-08 | |
| dc.date | 2007-06-27 | |
| dc.date.accessioned | 2026-07-07T08:12:33Z | |
| dc.date.available | 2026-07-07T08:12:33Z | |
| dc.description | A (smooth) K3 surface X defined over a field k of characteristic 0 is called singular if the Néron-Severi lattice NS (X) of X over the algebraic closure of k is of rank 20. Let X be a singular K3 surface defined over a number field F. For each embedding σof F into the complex number field, we denote by T(X^σ) the transcendental lattice of the complex K3 surface X^σobtained from X by σ. For each prime ideal P of F at which X has a supersingular reduction X_P, we define L(X, P) to be the orthogonal complement of NS(X) in NS(X_P). We investigate the relation between these lattices T(X^σ) and L(X, P). As an application, we give a lower bound of the degree of a number field over which a singular K3 surface with a given transcendental lattice can be defined. | |
| dc.description | 40 pages, revised version, to appear in Transactions of the American Mathematical Society | |
| dc.identifier | https://arxiv.org/abs/math/0611208 | |
| dc.identifier | http://arxiv.org/abs/math/0611208 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/132489 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14J28 | |
| dc.title | Transcendental lattices and supersingular reduction lattices of a singular $K3$ surface | |
| dc.type | text |