A REMARK ON THE DOUADY SEQUENCE FOR NON-PRIMARY HOPF MANIFOLDS

Abstract

To determine cohomology groups of holomorphic vector bundles or more general coherent analytic sheaves on complex manifolds is very important in several complex variables and complex geometry. For example, Cartan-Serre's theorem B and Kodaira's vanishing theorem are fundamental respectively in the studies of two classes of complex manifolds: Stein manifolds and projective algebraic manifolds. Deformation and moduli space of complex structures are also closely related to the determination of the cohomology groups of the bundles according to Kodaira-Spencer's theory