Transcendental lattices and supersingular reduction lattices of a singular K3 surface

By Ichiro Shimada. 2006

54 citations recorded by the source corpus.

A K3 surface X defined over a field k of characteristic 0 is called singular if the Neron-Severi lattice NS(X) of X ⊗ k is of rank 20. Let X be a singular K3 surface defined over a number field F. For each embedding σ: F → C, we denote by T(X") the transcendental lattice of the complex K3 surface X σ obtained from X by σ. For each prime p of F at which X has a supersingular reduction Xp, we define L(X,p) to be the orthogonal complement of NS(X) in NS(Xp). We investigate the relation between these lattices T(X σ ) and L(X,p). As an application, we give a lower bound for the degree of a number field over which a singular K3 surface with a given transcendental lattice can be defined.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/debb3bfe806b810d0746565d5d6a206eafe38f6a

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In Geometry and Topology

1. D. Huybrechts
2. E. Markman
3. Kieran G. O’Grady
4. P. Stellari
5. Emanuele Macrì
6. Keiji Oguiso
7. Ulrike Riess
8. Justin Sawon

In Mathematical Physics

1. D. Huybrechts
2. P. Stellari
3. Emanuele Macrì
4. E. Markman
5. Keiji Oguiso
6. Ulrike Riess
7. D. Joyce
8. Arend Bayer

Citations in the corpus

• Lectures on K3 Surfaces (2016, methodology): “15] and Shimada [551], on the right hand side one distinguishes the K3 surfaces S only up to conjugation.”