Localization of Atiyah classes

DOI10.4171/RMI/730zbMath1278.14006arXiv1005.1482OpenAlexW2045913732MaRDI QIDQ1955675

Marco Abate, Tatsuo Suwa, Francesca Tovena, Filippo Bracci

Publication date: 17 June 2013

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1005.1482

zbMATH Keywords

Chern classesAtiyah forms and classesAtiyah residuesBott type vanishing theoremsČech-Dolbeault cohomologyconnections of type (1, 0)localization and residuessingular holomorphic distributions

Mathematics Subject Classification ID

Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry (14C17) Characteristic classes and numbers in differential topology (57R20) Singularities of holomorphic vector fields and foliations (32S65) Connections (general theory) (53C05) Vector distributions (subbundles of the tangent bundles) (58A30) Dynamical aspects of holomorphic foliations and vector fields (37F75) Vanishing theorems (32L20) Residues for several complex variables (32A27)

Related Items (10)

Residues and Hyperfunctions ⋮ Relative Čech-Dolbeault homology and applications ⋮ Localization of Bott‐Chern classes and Hermitian residues ⋮ Sato hyperfunctions via relative Dolbeault cohomology ⋮ Representation of relative sheaf cohomology ⋮ Dynamical aspects of foliations with ample normal bundle ⋮ Note on Dolbeault cohomology and Hodge structures up to bimeromorphisms ⋮ \(\overline{\partial}\)-tangential invariants of certain vector bundles over complex foliations ⋮ Characteristic classes of Higgs bundles and Reznikov's theorem ⋮ Connections and \(L_\infty\) liftings of semiregularity maps

Cites Work

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• Singularities of holomorphic foliations
• Résidus des sous-variétés invariantes d'un feuilletage singulier. (Residues of invariant submanifolds of singular foliations)
• Hochschild cohomology and Atiyah classes
• Vector fields on singular varieties
• Invariant varieties through singularities of holomorphic vector fields
• Vector fields and Chern numbers
• Residual indices of holomorphic maps relative to singular curves of fixed points on surfaces
• The residual index and the dynamics of holomorphic maps tangent to the identity
• Index theorems for holomorphic self-maps
• Residues of holomorphic vector fields relative to singular invariant subvarieties
• Complex Analytic Connections in Fibre Bundles
• The Atiyah class, Hochschild cohomology and the Riemann-Roch theorem
• Index theorems for holomorphic maps and foliations
• Rozansky-Witten invariants via Atiyah classes
• Monodromy and topological classification of germs of holomorphic foliations

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