Singular holomorphic foliations
Başlık çevirisi mevcut değil.
- Tez No: 400275
- Danışmanlar: JAMES B. CARRELL
- Tez Türü: Doktora
- Konular: Matematik, Mathematics
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 1984
- Dil: İngilizce
- Üniversite: The University of British Columbia
- Enstitü: Yurtdışı Enstitü
- Ana Bilim Dalı: Matematik Ana Bilim Dalı
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 77
Özet
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Özet (Çeviri)
A generalized Nash Blow-up M0 with respect to coherent subsheaves of locallyfree sheaves is defined for complex spaces. It is shown that M0 is locally isomorphicto a monoidal transformation and hence is analytic. Examples of M0are given. Applications are given to Serre?s extension problem and reductivegroup actions. A C¤-action on Grassmannians is defined, fixed point sets andBialynicki-Birula decomposition are described. This action is generalized toGrassmann bundles. The Grassmann graph construction is defined for the analyticcase and it is shown that for a compact Kaehler manifold the cycle atinfinity is an analytic cycle. A calculation involving the localized classes ofgraph construction is given. Nash residue for singular holomorphic foliations isdefined and it is shown that the residue of Baum-Bott and the Nash residuediffer by a term that comes from the Grassmann graph construction of the singularfoliation. As an application conclusions are drawn about the rationalityconjecture of Baum-Bott. Pontryagin classes in the cohomology of the splittingmanifold are given which obstruct an imbedding of a bundle into the tangentbundle.
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