Moduli spaces of compact complex submanifolds of complex fibered manifolds

Abstract

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 isomorphismbetween 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.