Embeddings of submanifolds and normal bundles
| Autor: | Marco Abate, Filippo Bracci, Francesca Tovena |
|---|---|
| Rok vydání: | 2009 |
| Předmět: |
Mathematics - Differential Geometry
Pure mathematics 32S65 37F10 32A27 37F75 Mathematics(all) Mathematics - Complex Variables Mathematics::Complex Variables General Mathematics Mathematical analysis Splitting submanifolds Zero (complex analysis) Codimension Surface (topology) Submanifold Embeddings Section (fiber bundle) Normal bundle Differential Geometry (math.DG) Formal neighborhood FOS: Mathematics Embedding Settore MAT/03 - Geometria Complex manifold Complex Variables (math.CV) Mathematics |
| Zdroj: | Advances in Mathematics. 220(2):620-656 |
| ISSN: | 0001-8708 |
| DOI: | 10.1016/j.aim.2008.10.001 |
| Popis: | This paper is devoted to the study of the embeddings of a complex submanifold $S$ inside a larger complex manifold $M$; in particular, we are interested in comparing the embedding of $S$ in $M$ with the embedding of $S$ as the zero section in the total space of the normal bundle $N_S$ of $S$ in $M$. We explicitely describe some cohomological classes allowing to measure the difference between the two embeddings, in the spirit of the work by Grauert, Griffiths, and Camacho-Movasati-Sad; we are also able to explain the geometrical meaning of the separate vanishing of these classes. Our results holds for any codimension, but even for curves in a surface we generalize previous results due to Laufert and Camacho-Movasati-Sad. Comment: 29 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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