A simple proof of the surjectivity of the period map of K3 surfaces

DOI10.1007/BF01263265zbMath0497.32019OpenAlexW2024786149MaRDI QIDQ1170672

Yum-Tong Siu

Publication date: 1981

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/154797

zbMATH Keywords

moduli spaceCalabi conjectureperiod mapamplenesslocal Torelli theoremKaehler-Einstein metricKaehler K3 surfaces

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Complex-analytic moduli problems (32G13) Period matrices, variation of Hodge structure; degenerations (32G20) Moduli, classification: analytic theory; relations with modular forms (14J15) Compact complex surfaces (32J15) Special surfaces (14J25)

Related Items (20)

Cubic Fourfolds, K3 Surfaces, and Rationality Questions ⋮ Symplectic mapping class groups of K3 surfaces and Seiberg-Witten invariants ⋮ \(\mathrm{G}_2\) manifolds with nodal singularities along circles ⋮ Classification of Picard lattices of K3 surfaces ⋮ Examples of lattice-polarized K3 surfaces with automorphic discriminant, and Lorentzian Kac–Moody algebras ⋮ Classification of degenerations and Picard lattices of Kählerian \(K3\) surfaces with symplectic automorphism group \(C_4\) ⋮ Classification of degenerations of codimension \({\le}\,5\) and their Picard lattices for Kählerian \(K3\) surfaces with the symplectic automorphism group \((C_2)^2\) ⋮ Hilbert schemes of K3 surfaces are dense in moduli ⋮ Kummer surfaces associated with Seiberg-Witten curves ⋮ Finiteness and quasi-simplicity for symmetric \(K3\)-surfaces ⋮ Teichmüller spaces and Torelli theorems for hyperkähler manifolds ⋮ Gravitational instantons with faster than quadratic curvature decay. III. ⋮ Not doomed to fail ⋮ Classification of degenerations and Picard lattices of Kählerian K3 surfaces with symplectic automorphism group ⋮ A geometric approach to problems in birational geometry ⋮ The overarching finite symmetry group of Kummer surfaces in the Mathieu group \(M_{24}\) ⋮ Every K 3 surface is Kähler ⋮ On K3 surfaces with large Picard number ⋮ Degenerations of Kählerian K3 surfaces with finite symplectic automorphism groups. III ⋮ Kählerian K3 surfaces and Niemeier lattices. I

Cites Work

• Applications of the Kaehler-Einstein-Calabi-Yau metric to moduli of K3 surfaces
• Über Modifikationen und exzeptionelle analytische Mengen
• On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I
• On the Structure of Compact Complex Analytic Surfaces, I

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