Embeddings of submanifolds and normal bundles

2006/12/15 by Marco Abate, Filippo Bracci, Abate, Marco +3 · 2 citations
Mathematics · #32A27 #32S65 #37F10 #37F75 #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.math/0612449

openalex publication_date 2006/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 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.

Cited by

• On embedding theorems in analytic and harmonic function spaces of several variables in some domains in Cⁿ
• On the volume of K-semistable Fano manifolds

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