On the computation of the Picard group for K3 surfaces

DOI10.1017/S0305004111000326zbMath1223.14044arXiv1006.1724MaRDI QIDQ3089119

Andreas-Stephan Elsenhans, Jörg Jahnel

Publication date: 23 August 2011

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1006.1724

zbMATH Keywords

Picard groups of \(K3\) surfaces

Mathematics Subject Classification ID

(K3) surfaces and Enriques surfaces (14J28) Varieties over global fields (11G35) Arithmetic ground fields for surfaces or higher-dimensional varieties (14J20)

Related Items (12)

On the distribution of the Picard ranks of the reductions of a \(K3\) surface ⋮ Unnamed Item ⋮ Transcendental obstructions to weak approximation on general \(K3\) surfaces ⋮ Arithmetic of K3 Surfaces ⋮ Kummer surfaces and the computation of the Picard group ⋮ Picard numbers of quintic surfaces ⋮ A Numerical Transcendental Method in Algebraic Geometry: Computation of Picard Groups and Related Invariants ⋮ Good reduction criterion for \(K3\) surfaces ⋮ Variation of Néron–Severi Ranks of Reductions of K3 Surfaces ⋮ Failure of the Hasse principle on general surfaces ⋮ Computing Néron–Severi groups and cycle class groups ⋮ On the geometry of K3 surfaces with finite automorphism group and no elliptic fibrations

Cites Work

• Unnamed Item
• Cubic surfaces with a Galois invariant double-six
• \(K3\) surfaces with Picard number one and infinitely many rational points
• On a conjecture of Artin and Tate
• On the Brauer group of a surface
• La conjecture de Weil. I
• K3 Surfaces of Picard Rank One and Degree Two
• Elliptic K3 Surfaces with Geometric Mordell–Weil Rank 15
• Numerical and Homological Equivalence of Algebraic Cycles on Hodge Manifolds

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