Néron models and limits of Abel–Jacobi mappings

DOI10.1112/S0010437X09004400zbMath1195.14006OpenAlexW2172071899WikidataQ57445974 ScholiaQ57445974MaRDI QIDQ3552177

Phillip A. Griffiths, Matthew Kerr, Mark L. Green

Publication date: 13 April 2010

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

Full work available at URL: https://doi.org/10.1112/s0010437x09004400

zbMATH Keywords

polarizationNéron modelmotivic cohomologyAbel-Jacobi mapCeresa cyclelimit mixed Hodge structurealgebraic cyclesemistable reductionvariation of Hodge structureadmissible normal functionunipotent monodromyhigher Chow cycleClemens-Schmid sequenceslit analytic space

Mathematics Subject Classification ID

Fibrations, degenerations in algebraic geometry (14D06) Variation of Hodge structures (algebro-geometric aspects) (14D07) Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) (14F43) Algebraic cycles (14C25) Transcendental methods, Hodge theory (algebro-geometric aspects) (14C30) Motivic cohomology; motivic homotopy theory (14F42) Applications of methods of algebraic (K)-theory in algebraic geometry (14C35)

Related Items

Algebraic and Arithmetic Properties of Period Maps, Sections of Calabi-Yau threefolds with K3 fibration, Limits and singularities of normal functions, Néron models in log mixed Hodge theory by weak fans, A variant of Néron models over curves, Complex analytic Néron models for arbitrary families of intermediate Jacobians, Néron models of Green-Griffiths-Kerr and log Néron models, Néron models of intermediate Jacobians associated to moduli spaces, Simplicial Abel-Jacobi maps and reciprocity laws, Néron models for admissible normal functions, Vanishing cycle sheaves of one-parameter smoothings and quasi-semistable degenerations, Log intermediate Jacobians, Lectures on Hodge theory and algebraic cycles, Zero loci of admissible normal functions with torsion singularities, NORMAL FUNCTIONS FOR ALGEBRAICALLY TRIVIAL CYCLES ARE ALGEBRAIC FOR ARITHMETIC REASONS, Degeneration of intermediate Jacobians and the Torelli theorem, Classifying spaces of degenerating mixed Hodge structures, III: Spaces of nilpotent orbits

Cites Work

• Variation of mixed Hodge structure. I
• Log complexes of currents and functorial properties of the Abel-Jacobi map
• The zero locus of an admissible normal function
• Algebraic cycles on certain desingularized nodal hypersurfaces
• C is not algebraically equivalent to \(C^-\) in its Jacobian
• Singularities of admissible normal functions (with an appendix by Najmuddin Fakhruddin)
• Lines on complete intersection threefolds with \(K=0\)
• A study of variation of mixed Hodge structure
• 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
• Degeneration of Kähler manifolds
• Toroidal degeneration of abelian varieties
• Variation of Hodge structure: The singularities of the period mapping
• Degenerations of quintic threefolds and their lines
• Degenerations of mixed Hodge structure.
• \(\text{SL}_2\)-orbits and degenerations of mixed Hodge structure
• The Abel-Jacobi map for higher Chow groups. II
• The currents defined by analytic varieties
• Slicing and intersection theory for chains associated with real analytic varieties
• On compact analytic surfaces. II
• Global Residues and Intersections on a Complex Manifold
• Maximal unipotent monodromy for complete intersection CY manifolds
• The Abel–Jacobi map for higher Chow groups