Every rational Hodge isometry between two K3 surfaces is algebraic

DOI10.1515/crelle-2017-0027zbMath1475.32008arXiv1510.02852OpenAlexW2962838810MaRDI QIDQ2331061

Nikolay Buskin

Publication date: 24 October 2019

Published in: Journal für die Reine und Angewandte Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.02852

zbMATH Keywords

\(K3\) surfacesHodge isometry

Mathematics Subject Classification ID

(K3) surfaces and Enriques surfaces (14J28) Algebraic dependence theorems (32J10)

Related Items (14)

Explicit coverings of families of elliptic surfaces by squares of curves ⋮ On prime degree isogenies between \(K3\) surfaces ⋮ Twisted derived equivalences and isogenies between \(K3\) surfaces in positive characteristic ⋮ Hodge similarities, algebraic classes, and Kuga-Satake varieties ⋮ Sixfolds of generalized Kummer type and K3 surfaces ⋮ The monodromy of generalized Kummer varieties and algebraic cycles on their intermediate Jacobians ⋮ A motivic global Torelli theorem for isogenous \(K3\) surfaces ⋮ Complex multiplication and Brauer groups of \(K3\) surfaces ⋮ Twistor lines in the period domain of complex tori ⋮ On certain isogenies between K3 surfaces ⋮ CM liftings of surfaces over finite fields and their applications to the Tate conjecture ⋮ Fields of definition of \(K3\) surfaces with complex multiplication ⋮ Rigid hyperholomorphic sheaves remain rigid along twistor deformations of the underlying hyparkähler manifold ⋮ Motives of isogenous \(K3\) surfaces

Cites Work

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• On the Hodge conjecture for products of certain surfaces
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• Erratum to: Compact hyperkähler manifolds: basic results
• A survey of Torelli and monodromy results for holomorphic-symplectic varieties
• ON CORRESPONDENCES BETWEEN K3 SURFACES
• INTEGRAL SYMMETRIC BILINEAR FORMS AND SOME OF THEIR APPLICATIONS
• On the Torelli problem for kählerian $K-3$ surfaces
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• The standard conjectures for holomorphic symplectic varieties deformation equivalent to Hilbert schemes ofK3 surfaces
• On the monodromy of moduli spaces of sheaves on K3 surfaces
• A TORELLI THEOREM FOR ALGEBRAIC SURFACES OF TYPEK3
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