Defect relations for holomorphic maps between spaces of different dimensions

DOI10.1215/S0012-7094-87-05512-8zbMath0623.32018MaRDI QIDQ1091521

Yum-Tong Siu

Publication date: 1987

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

zbMATH Keywords

second fundamental formdivisorKähler surfaceconnectioncomplex manifoldholomorphic line bundlemeromorphic mapdefect relation for holomorphic mappings

Mathematics Subject Classification ID

Holomorphic mappings and correspondences (32H99) Holomorphic bundles and generalizations (32L05) Value distribution theory in higher dimensions (32H30)

Related Items (14)

On Griffiths–Lang's conjecture and related topics ⋮ Algebraic families of smooth hyperbolic surfaces of low degree in \(\mathbb{P}_ \mathbb{C}^ 3\) ⋮ A uniqueness theorem for holomorphic mappings in the disk sharing totally geodesic hypersurfaces ⋮ The second Main theorem for meromorphic mappings into a complex projective space ⋮ The second main theorem of hypersurfaces in the projective space ⋮ Value distribution of meromorphic mappings into compactified locally symmetric spaces ⋮ On the hyperbolicity of general hypersurfaces ⋮ Vector fields on the total space of hypersurfaces in the projective space and hyperbolicity ⋮ Hyperbolic surfaces in \({\mathbb{P}}^ 3\) ⋮ Recent results on the Kobayashi and Green-Griffiths-Lang conjectures ⋮ Nonequidimensional value distribution theory and meromorphic connections ⋮ The second main theorem of holomorphic curves into projective spaces ⋮ Holomorphic mappings between spaces of different dimensions. II ⋮ The second main theorem for holomorphic curves into semi-Abelian varieties

Cites Work

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• Nevanlinna defect relations for singular divisors
• Holomorphic curves and metrics of negative curvature
• Holomorphic curves in algebraic varieties
• Value distribution of holomorphic maps into compact complex manifolds
• A defect relation for equidimensional holomorphic mappings between algebraic varieties
• Meromorphic curves
• A Hypersurface Defect Relation for a Class of Meromorphic Maps
• Some Picard Theorems for Holomorphic Maps to Algebraic Varieties

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