Rational curves on \(K3\) surfaces

DOI10.1007/s00222-011-0359-yzbMath1255.14026arXiv1012.3777OpenAlexW2006810424MaRDI QIDQ431136

Christian Liedtke, Jun Li

Publication date: 26 June 2012

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1012.3777

zbMATH Keywords

rational curves\(K3\) surfacestable mapsrigidifier

Mathematics Subject Classification ID

(K3) surfaces and Enriques surfaces (14J28) Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) (14N35) Positive characteristic ground fields in algebraic geometry (14G17)

Related Items (12)

Exceptional jumps of Picard ranks of reductions of K3 surfaces over number fields ⋮ On the distribution of the Picard ranks of the reductions of a \(K3\) surface ⋮ 24 Rational curves on K3 surfaces ⋮ Rational curves on general type hypersurfaces ⋮ Kontsevich spaces of rational curves on Fano hypersurfaces ⋮ \(\mathbb{A}^1\) curves on log \(K3\) surfaces ⋮ \({\mathbb A}^1\)-curves on affine complete intersections ⋮ Low-dimensional projective manifolds with nef tangent bundle in positive characteristic ⋮ Variation of Néron–Severi Ranks of Reductions of K3 Surfaces ⋮ Curves on \(K3\) surfaces ⋮ Curves of maximal moduli on K3 surfaces ⋮ Hyper-Kähler manifolds

Cites Work

• Constructing rational curves on \(K3\) surfaces
• The Tate conjecture for ordinary K 3 surfaces over finite fields
• Ordinary reduction of K3 surfaces
• Tate's conjecture for \(K3\) surfaces of finite height
• Algebraic construction of Brieskorn's resolutions
• Compactifying the space of stable maps
• Supersingular $K3$ surfaces
• Formal groups arising from algebraic varieties
• Genus Change in Inseparable Extensions of Function Fields
• Density of rational points on elliptic \(K3\) surfaces
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