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Embeddings of submanifolds and normal bundles

Advances in Mathematics, ISSN: 0001-8708, Vol: 220, Issue: 2, Page: 620-656
2009
  • 12
    Citations
  • 0
    Usage
  • 4
    Captures
  • 0
    Mentions
  • 0
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Metric Options:   Counts1 Year3 Year

Metrics Details

  • Citations
    12
    • Citation Indexes
      12
  • Captures
    4

Article Description

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.

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