On Stability of Compact Submanifolds of Complex Manifolds
Kunihiko Kodaira
Jan 1961 · Mathematical Sciences Directorate, Air Force Office of Scientific Research
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Stability of compact submanifolds of complex manifolds and some related topics are discussed. A compact submanifold V of a complex manifold W is said to be stable if any small deformation W T OF contains a small deformation Vt of V. Let psi be the sheaf over V of germs of holomorphic sections of the normal bundle of V in W. If the first cohomology group H1(V, psi) vanishes then V is a stable submanifold of W.A fibre structure of a compact fibred complex manifold M is said to be stable if any small deformation Mt of M retains a fibre structure. If each fibre of M is regular then the fibre structure of M is stable. (Author).
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