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Residues of Chern classes
| Title: | Residues of Chern classes |
| Authors: | Suwa, T. Browse this author |
| Issue Date: | May-2001 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 525 |
| Start Page: | 1 |
| End Page: | 20 |
| Abstract: | 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 Poincare 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 expresses the residues in terms of Grothendieck residues relative to the subvariety. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69275 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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