Project/Area Number  08454007 
Research Category 
GrantinAid for Scientific Research (B)

Section  一般 
Research Field 
Algebra

Research Institution  HIROSHIMA UNIVERSITY 
Principal Investigator 
SUMIHIRO Hideyasu Hiroshima Univ., Math.Dapart., Professor, 理学部, 教授 (60068129)

CoInvestigator(Kenkyūbuntansha) 
YOSHIOKA Kouta Hiroshima Univ., Math.Dapart., Asistant, 理学部, 助手 (40274047)
FURUSHIMA Mikio Hiroshima Univ., Integrated Arts and Sciences, Professor, 総合科学部, 教授 (00165482)
MATSUMOTO Keishi Hiroshima Univ., Math.Dapart., Assist.Professor, 理学部, 助教授 (30229546)
SUGANO Takashi Hiroshima Univ., Math.Dapart., Assist.Professor, 理学部, 助教授 (30183841)
TANISAKI Toshiyuki Hiroshima Univ., Math.Dapart., Professor, 理学部, 教授 (70142916)

Project Fiscal Year 
1996 – 1996

Project Status 
Completed(Fiscal Year 1996)

Budget Amount *help 
¥4,700,000 (Direct Cost : ¥4,700,000)
Fiscal Year 1996 : ¥4,700,000 (Direct Cost : ¥4,700,000)

Keywords  Vector Bundles / Moduli Spaces / Quantum Groups / DModules / Hypergeometric Functions / Modular Forms / Hodge Theory / Moishezon Manifolds / ベクトル束 / モジュライ空間 / 量子群 / D加群 / 超幾何関数 / 保型形式 / Hodge理論 / モイレェゾニ多様体 / モイレェゾン多様体 
Research Abstract 
In this project, we studied vector bundles on manifolds from the following various points of view : 1)algebraic geometric method, 2)algebraic analytic method, 3)number theoretic method. In 1), we obtained (1) a necessary and sufficient condition for a rank 2 bundle on projective space P^n (n*4) to split into line bundles which gives us a new approach to important conjectures concerning splitting of vector bundles on P^n, (2) we classified Nonprojective Moishezon compactifications (X,Y) of affine C^3 space by clarifing numerically effectiveness of the boundary divisor Y and moreover, showed an equivalence between the Stein ess of a C^1 fiber space over a nonStein manifold S and the triviality of certain rank 2 bundle on S., (3) we proved under some conditions on the first Chern class, the rationality of the moduli of bundles on surfaces with elliptic curves as fibers and have determined the Picard group and Albanese map of the moduli of bundles on elliptic surfaces. In 2), we studied
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(1) heighest weight modules of semisimple Lie algebras, especially those corresponding to compact Hermitian symmetric spaces, (2) we have introduced the definition of Radon transformation on Flag manifolds of general type and founed usefulness of bundles to study the Radon transformation, (3) we got a duality concerning generalized hypergeometric functions by using the intersection theory on twisted cohomology group and the exterior products. In 3), (1) we gave an expression by integrals in terms of their Fourier coefficients of the Lfunctions which are liftings of cusp forms with haif integer weights to the modular forms on orthogonal groups and proved the meromorphic continuation and the functional equation under some technical conditions which can be viewed as a generalization of KohnenSkoruppa's result on quadratic Siegel cusp forms, (2) we showed an categorical equivalence between the category of padic Galoi representations over local fields with positive characteristic and the category of etale differential modules with Frobenius map and in particular, the ones whose representation of inertial group factors through finite representations correspond to overconvergent modules, (3) investigated sheaficatin of padic Hodge theory and their relativeness, which are analogue to RiemannHilbert correspondence in the case of complex manifolds. Less
