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Moduli spaces of compact complex submanifolds of complex fibered manifolds

Published online by Cambridge University Press:  24 October 2008

Sergey A. Merkulov
Sergey A. Merkulov
Affiliation:
School of Mathematics and Statistics, University of Plymouth, Plymouth, Devon PL4 8AA
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Extract

In 1962 Kodaira[11] proved that ifX ↪ Y is a compact complex submanifold with normal bundle N such that H1(X, N) = 0, then X belongs to a locally complete family {Xt: t ∈ M} of complex submanifolds Xt of Y with the moduli space M being a (dimcH0(X, N))-dimensional complex manifold, and there exists a canonical isomorphism

between the tangent space of M at a point t ∈ M and the space of all global sections of the normal bundle Nt of the embedding Xt ↪ Y.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 118 , Issue 1 , July 1995 , pp. 71 - 91
Copyright
Copyright © Cambridge Philosophical Society 1995

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