Recovery of vanishing cycles by log geometry

DOI10.2748/tmj/1178207529zbMath1015.14005OpenAlexW2071903814MaRDI QIDQ5937392

Sampei Usui

Publication date: 5 August 2003

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2748/tmj/1178207529

zbMATH Keywords

integral structure of the degenerate variation of mixed Hodge structurelog geometryrecovery of vanishing cyclesRiemann-Hilbert correspondence

Mathematics Subject Classification ID

Period matrices, variation of Hodge structure; degenerations (32G20) Variation of Hodge structures (algebro-geometric aspects) (14D07) Algebraic cycles (14C25) Transcendental methods, Hodge theory (algebro-geometric aspects) (14C30)

Related Items

Relative rounding in toric and logarithmic geometry ⋮ Signs in weight spectral sequences, monodromy-weight conjectures, log Hodge symmetry and degeneration of surfaces ⋮ Degenerations of log Hodge de Rham spectral sequences, log Kodaira vanishing theorem in characteristic \(p>0\) and log weak Lefschetz conjecture for log crystalline cohomologies ⋮ Examples of non-Kähler Calabi-Yau 3-folds with arbitrarily large \(b_2\) ⋮ Log intermediate Jacobians ⋮ Mixed Hodge structures on log deformations ⋮ On log Hodge structures of higher direct images ⋮ Images of extended period maps

Cites Work

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• Variation of Hodge structure: The singularities of the period mapping
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• The relative log Poincaré lemma and relative log de Rham theory