Constructing rational curves on \(K3\) surfaces

DOI10.1215/00127094-1272930zbMath1236.14035arXiv0907.3527OpenAlexW2950862457MaRDI QIDQ544672

Yuri Tschinkel, Brendan Hassett, Fedor A. Bogomolov

Publication date: 15 June 2011

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0907.3527

zbMATH Keywords

rational curves\(K3\) surfaces

Mathematics Subject Classification ID

(K3) surfaces and Enriques surfaces (14J28) Families, moduli of curves (algebraic) (14H10) Arithmetic ground fields (finite, local, global) and families or fibrations (14D10) Formal methods and deformations in algebraic geometry (14D15)

Related Items (18)

Exceptional jumps of Picard ranks of reductions of K3 surfaces over number fields ⋮ Deformations of rational curves in positive characteristic ⋮ On RC varieties without smooth rational curves ⋮ Betti numbers of curves and multiple-point loci ⋮ Lines on quartic surfaces ⋮ On the distribution of the Picard ranks of the reductions of a \(K3\) surface ⋮ Rational curves on elliptic surfaces ⋮ 24 Rational curves on K3 surfaces ⋮ Families of rational curves on holomorphic symplectic varieties and applications to 0-cycles ⋮ Rational curves on \(K3\) surfaces ⋮ Density of rational curves on \(K3\) surfaces ⋮ \(\mathbb{A}^1\) curves on log \(K3\) surfaces ⋮ On \(W_2\)-lifting of Frobenius of algebraic surfaces ⋮ The moduli of singular curves on \(K3\) surfaces ⋮ Variation of Néron–Severi Ranks of Reductions of K3 Surfaces ⋮ Curves on \(K3\) surfaces ⋮ Curves of maximal moduli on K3 surfaces ⋮ Higher Chow cycles on Abelian surfaces and a non-Archimedean analogue of the Hodge--conjecture

Cites Work

• The Picard group of a \(K3\) surface and its reduction modulo \(p\)
• Néron-Severi groups under specialization
• The Tate conjecture for ordinary K 3 surfaces over finite fields
• Ordinary reduction of K3 surfaces
• Surfaces of type K3 over fields of finite characteristic
• Tate's conjecture for \(K3\) surfaces of finite height
• La conjecture de Weil pour les surfaces K3
• Semi-regularity and de Rham cohomology
• Compactifying the space of stable maps
• Deformations of Algebraic Schemes
• Projective Models of K - 3 Surfaces
• Supersingular $K3$ surfaces
• On weights of the $ l$-adic representation and arithmetic of Frobenius eigenvalues
• Families of rationally connected varieties
• Rational curves and points on K3 surfaces
• Density of rational points on elliptic \(K3\) surfaces
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