Study of the stability theory of polarized compact Kahler manifolds

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We have obtained the following results concerning our research project.l. A. Fujiki : (1)has introduced a hyper kahler structure on the module space of representations of the fundamental group of a compact Kahler manifold and has studied, its properties, (2)has studied the existence and the uniquenss of extremal Kahler metrics on a ruled manifolds, (3)has shown an L Dolbeault lemma on a quasi-projective manifold and given its applications to deformations of locally symmetric varieties and to the existence of a Kahler-Einstein metric, and(4)has constructed a natural parabolic sheaf starting from a hermitian vector bundle with certain curvature growth condition defined on a quasi-projective manifold.2. M. Ue has determined the differentiable and geometric structures. together with the deformations of the latter on certain general 4-dimensional Sei Seifert fiber spaces and has also found some exotic differentiable structures, Where the study of elliptic surfaces is especially relevant.3. T. Ueda has studied the iterations of analytic transformations with parabolic fixed point set. Further, he has obtained a condition for a rational curve with a node in a complex surface to admit a strongly pseudoconcave neighborhood. 4. A. Gyouia has given general and explict methods of constructing relative invariants on a prehomogeneous vector space, computing their Fourier transforms and b-functions. Moreover, he has given a counter-example concerning the group action on such a vector space, and developped a representation of theory of group schems 5. H. Saito has given the classification and the product formula for the representations of quaternion algebras over local fields, with a trace formula for a certain Hecke operator as its application. He has also given the characters of the admissible representations of GL(2)via the theory of base change.