On Deformations of Complex Analytic Structures |
Common terms and phrases
abelian algebraic surface arbitrary B-forms biregular biregularly bundle deformation Chern class cohomology commutative diagram compact complex manifold complex analytic family complex fibre bundles complex line bundle complex manifolds complex structures complex tori coordinates defined DEFINITION deformation space deformations of complex denote differentiable family differentiable map differentiable sections dim H°(V effectively parametrized element exact sequence exists family of complex fibre bundles fibre Vt follows forms of type germs of differentiable germs of holomorphic graded Lie algebra H¹ Vt H¹(V H¹(Vt Hence holomorphic functions holomorphic sections Hopf manifold induced isomorphism Kähler manifold Kodaira lemma Lie algebra linear metric Moreover neighborhood non-singular number of moduli obtain principal bundles PROOF Proposition regular map restriction sheaf of germs sheaves structure group submanifolds subsheaf subspace sufficiently small tangent bundle Theorem TM)t trivial U₁ vector bundle vector fields