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 NS 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.

Abate, M., Bracci, F., Tovena, F. (2009). Embeddings of submanifolds and normal bundles. ADVANCES IN MATHEMATICS, 220(2), 620-656 [10.1016/j.aim.2008.10.001].

Embeddings of submanifolds and normal bundles

BRACCI, FILIPPO;TOVENA, FRANCESCA
2009-01-01

Abstract

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 NS 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.
2009
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/03 - GEOMETRIA
English
Abate, M., Bracci, F., Tovena, F. (2009). Embeddings of submanifolds and normal bundles. ADVANCES IN MATHEMATICS, 220(2), 620-656 [10.1016/j.aim.2008.10.001].
Abate, M; Bracci, F; Tovena, F
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/60091
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