Log complexes of currents and functorial properties of the Abel-Jacobi map

DOI10.1215/S0012-7094-83-05001-9zbMath0526.32011MaRDI QIDQ595066

James R. King

Publication date: 1983

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

zbMATH Keywords

Hodge filtrationAbel-Jacobi mapintermediate Jacobiancompact Kaehler varietylog complexes of currents

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Analytic sheaves and cohomology groups (32C35) Picard schemes, higher Jacobians (14K30) Sheaves and cohomology of sections of holomorphic vector bundles, general results (32L10) Transcendental methods, Hodge theory (algebro-geometric aspects) (14C30) Integration on analytic sets and spaces, currents (32C30)

Related Items

Regulator maps for higher Chow groups via current transforms ⋮ The Abel-Jacobi map for higher Chow groups. II ⋮ Néron models and limits of Abel–Jacobi mappings ⋮ Semi-algebraic chains on projective varieties and the Abel-Jacobi map for higher Chow cycles ⋮ A commutative regulator map into Deligne-Beilinson cohomology ⋮ Deligne homology and Abel-Jacobi maps ⋮ Lectures on Hodge theory and algebraic cycles ⋮ Higher Chow groups and the Hodge-\({\mathcal D}\)-conjecture ⋮ A BSD formula for high-weight modular forms

Cites Work

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• Fundamental solutions in complex analysis. I. The Cauchy Riemann operator
• Hodge theory with degenerating coefficients: \(L_2\) cohomology in the Poincaré metric
• Limits of Hodge structures
• Generalized intermediate Jacobians and the theorem on normal functions
• On deformations of complex analytic structures. I
• Tangents to an analytic variety
• Periods of integrals on algebraic manifolds. III: Some global differential-geometric properties of the period mapping
• On the periods of certain rational integrals. I, II
• The currents defined by analytic varieties
• Residues and principal values on complex spaces
• A Theorem Concerning the Differential Equations Satisfied by Normal Functions Associated to Algebraic Cycles
• Global Residues and Intersections on a Complex Manifold
• Higher Picard Varieties
• Periods of integrals on algebraic manifolds: Summary of main results and discussion of open problems
• Sur le problème de la division