This paper studies the embeddings of a complex submanifold S inside a 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 explicitly 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 and Sad; we are also able to explain the geometrical meaning of the separate vanishing of these classes. Our results hold for any codimension, but even for curves in a surface we generalize previous results due to Laufert and Camacho, Movasati and Sad. (C) 2008 Elsevier Inc. All rights reserved.
|Autori:||Abate M; Bracci F; Tovena F|
|Titolo:||Embeddings of submanifolds and normal bundles|
|Anno del prodotto:||2009|
|Digital Object Identifier (DOI):||10.1016/j.aim.2008.10.001|
|Appare nelle tipologie:||1.1 Articolo in rivista|