Hodge similarities, algebraic classes, and Kuga-Satake varieties

DOI10.1007/s00209-023-03390-8arXiv2304.02519OpenAlexW4388417499MaRDI QIDQ6071891

Mauro Varesco

Publication date: 29 November 2023

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2304.02519

Mathematics Subject Classification ID

(K3) surfaces and Enriques surfaces (14J28) Hyper-Kähler and quaternionic Kähler geometry, ``special geometry (53C26) Transcendental methods, Hodge theory (algebro-geometric aspects) (14C30) Deformations of analytic structures (32G99) Mixed Hodge theory of singular varieties (complex-analytic aspects) (32S35) Holomorphic symplectic varieties, hyper-Kähler varieties (14J42)

Cites Work

• The Hodge conjecture for self-products of certain \(K3\) surfaces
• Nikulin involutions on \(K3\) surfaces
• On the Shafarevich and Tate conjectures for hyperkähler varieties
• Hyper-Kähler manifolds of generalized Kummer type and the Kuga-Satake correspondence
• Footnotes to papers of O'Grady and Markman
• Every rational Hodge isometry between two K3 surfaces is algebraic
• Motives of isogenous \(K3\) surfaces
• Symplectic automorphisms of prime order on \(K3\) surfaces
• Bloch's conjecture for Catanese and Barlow surfaces
• Real multiplication on \(K3\) surfaces and Kuga-Satake varieties
• Abelian varieties attached to polarized \(K_3\)-surfaces
• Lectures on K3 Surfaces
• The standard conjectures for holomorphic symplectic varieties deformation equivalent to Hilbert schemes ofK3 surfaces
• Compact Tori Associated to Hyperkähler Manifolds of Kummer Type
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