## On deformations of complex analytic structures |

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### Contents

DEFINITIONS HARMONIC FORMS ALONG THE FIBRES | 6 |

Local structure of a differentiable family | 43 |

GENERAL THEORY OF DEFORMATIONS OF COMPLEX | 59 |

7 other sections not shown

### Common terms and phrases

abelian algebraic surface analytic automorphisms arbitrary biregularly bundle deformation Chern class cohomology commutative diagram compact complex manifold complex analytic family complex analytic sense complex dimension complex fibre bundles complex line bundle complex manifolds complex structures complex tori coordinates defined DEFINITION deformation space denote differentiable family differentiable map differentiable sections dim H1 effectively parametrized element exact sequence exists family of complex fibre bundles fibre space fibre Vt follows forms of type germs of differentiable germs of holomorphic graded Lie algebra H1 VQ H1 Vt holomorphic functions holomorphic sections Hopf manifold induced infer infinitesimal deformation isomorphism Kahler manifold Kodaira lemma m(Vt maps each fibre metric Moreover non-singular number of moduli Pn+1 point t e principal bundles PROOF Proposition regular map restriction satisfies sheaf of germs sheaves space of infinitesimal structure group submanifolds subsheaf subspace tangent bundle Theorem TM)t trivial vector bundle vector fields