Kuranishi family of vector bundles and algebraic description of the moduli space of Einstein-Hermitian connections
The main purposes of this paper are to give a complete generalisation of the deformation theory of Kuranishi type for vector bundles and to prove that the differential geometric way and the algebra-geometric way of defining complex structures of the moduli space of irreducible Einstein- Hermitian connections give structures which are isomorphic to each other. Using Banach analytic space arguments the author shows the existence of a semi-universal local family of holomorphic structures and by a power series argument that the obtained family induces that of holomorphic vector bundles. Then he proves that, over a projective algebraic manifold, the analytic moduli space of simple holomorphic structures on a differentiable complex vector bundle \({\mathcal E}\) and the underlying complex space of the moduli space of simple algebraic vector bundles differentiably equivalent to \({\mathcal E}\) are isomorphic to each other. Finally he obtains the isomorphism of the two structures of the moduli space of irreducible Einstein-Hermitian connections and that the forgetful map from this moduli space into that of simple holomorphic structures is an open embedding as not necessarily reduced real analytic spaces.
irreducible Einstein-Hermitian connections
scientific article; zbMATH DE number 4118711
scientific article