Embeddings of submanifolds and normal bundles

• Autores: Marco Abate, Filippo Bracci, Francesca Tovena
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 220, Nº 2, 2009, págs. 620-656
• Idioma: inglés
• DOI: 10.1016/j.aim.2008.10.001
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• Resumen

  • 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 NS 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.