Classification and structure of polarized varieties

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The head investigator Fujita has classified non-singular polarized threefolds with Kodaira energy less than -1/2, and described precisely the structure of the adjoint fibrations. He further found out that the techniques of Kawachi-Masek in the study of base points of adjoint linear systems of normal polarized surfaces can be utilized also in the case of normal surfaces with Q-boundaries.Investigator Ishii has found a sufficient condition for minimal models of singularities of certain type to be obtained by a weighted blow up, and proved that nondegenerate hypersurface singularities have minimal, canonical and log-canonical models. She further found a counter example to a conjecture by Reid on a characterization of hypersurface rational singularities by weights, and showed the existence of simple elliptic singularies not of known type. She showed also various important properties of the set of possible values of the invariant - KィイD12ィエD1 of normal surface singularities.Investigator Tsu … More ji has established the theory of analytic Zariski decomposition, and constructed natural singular Hermitian metrics with positive curvature for line bundles. He applied this theory in the study of pluri-canonical systems of varities of general type and many problems including the abundance conjecture for minimal varieties of any dimensions.Investigator Mizumoto has showed that there are good Eisenstein liftings between certain spaces of (quasi)-automorphic forms. He further showed various properties of certain L-functions and non-regular Eisenstein series related to SL(2, Z).Investigator Nakayama has generalized classical theoris of etale cohomology to logarithmic structures. Further, he established basic theories of log geometry of complex analytic spaces, which was used to prove the degeneration of l-adic weight spectral sequences over arbitrary fields.Investigator Kobayashi has studied the behaviours of real algebraic varieties under blowing up, especially in case of embedded curves in real plane. He also constructed an explicit example of a Calabi-Yau threefold with certain elliptic fibration whose set of real points is a SUSY 3-torus. Less