Residues of Chern classes

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概要

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• If we have a finite number of sections of a complex vector bundle E over a manifold M, certain Chern classes of E are localized at the singular set S, i.e., the set of points where the sections fail to be linearly independent. When S is compact, the localizations define the residues at each connected component of S by the Alexander duality. If M itself is compact, the sum of the residues is equal to the Poincaré dual of the corresponding Chern class. This type of theory is also developed for vector bundles over a possibly singular subvariety in a complex manifold. Explicit formulas for the residues at an isolated singular point are also given, which express the residues in terms of Grothendieck residues relative to the subvariety.

• Mathematical Society of Japanの論文
• 2003-01-01

著者

• Suwa Tatsuo

  Department Of Mathematics Hokkaido University

• Tatsuo Suwa

  Department Of Mathematics Hokkaido University

関連論文

• RESIDUES OF HOLOMORPHIC VECTOR FIELDS RELATIVE TO SINGULAR INVARIANT SUBVARIETIES(Singularities of Holomorphic Vector Fields and Related Topics)
• INDICES AND RESIDUES OF HOLOMORPHIC VECTOR FIELDS ON SINGULAR VARIETIES(Topology of Holomorphic Dynamical Systems and Related Topics)
• CHERN CLASSES OF LOCAL COMPLETE INTERSECTIONS WITH ISOLATED SINGULARITIES(Singularities and Complex Analytic Geometry)
• Residues of Chern classes

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