1996 Fiscal Year Final Research Report Summary
Orenall Study on Algebraic Varieties and its Applications
| Project/Area Number |
07304002
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (A)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 総合 |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | University of Tokyo |
|---|
Principal Investigator |
KATSURA Toshiyuki Univ. of Tokyo Graduate School of Math. Sci. Professor, 大学院・数理科学研究科, 教授 (40108444)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
MUKAI Shigeru Nagoya Univ. Graduate School of Polymathematics Professor, 大学院多元数理科学研究科, 教授 (80115641)
SAKAI Fumio Saitama Univ. Department of Math. Professor, 理学部, 教授 (40036596)
MORI Shigefumi Kyoto Univ. Research Inst. of Math. Sci. Professor, 数理解析研究所, 教授 (00093328)
MIYANISHI Masayoshi Osaka Univ. Department of Math. Professor, 大学院理学研究科, 教授 (80025311)
FUJITA Takao Tokyo Inst. of Tech. Department of Math. Professor, 理学部, 教授 (40092324)
|
|---|
| Project Period (FY) |
1995 – 1996
|
| Keywords | algebraic geemetry / code / moduli space / Hamming code / polarigation / Calabi-Yau manifold / K3 surface / Mordell-Weil lattice |
|---|
| Research Abstract |
T.Katsura mainly studied the relation between algebraic geometry in positive characteristic and coding theory. He got notions of complete isolatedness and isolated radius. He showed that the [7,4,3]-hamming code is completely isolated and that its isolated radius is equal to 2ROO<2>/77. He also examined the Golay code with J.katsuta and almost finished their calculation. T.Fujita classified the polarized threefolds with Kodaira energy less than-1/2. Y.Kawamata treated Fujita's conjecture on ample line bundles and got the affirmative answer to it for three and four dimensional cases. He also investigated the cone consisted of divisors of a Calabi-Yau manifold, and showed that there exist at most finitely many minimal models for threefolds with positive Kadaira dimension. M.Maruyama studied the moduli space of semi-stable vector bundles, and showed the connectedness of the moduli space of instantons. He also succeeded in the construction of moduli space of stable sheaves. M.Miyanishi got a simple proof of the counter example by Roberts to the fourteenth problem of Hilbert, and also got some results on open algebraic varieties. S.Mori considered the action of flate group schemes on algebraic spaces, and got a general result on the existence of the quotients. Y.Morita studied rational points of algebraic surfaces and got some results on Batirev-Manin's conjecture. T.Shioda studied Mordell-Weil lattices, and as an application, he got algebraic curves of genus 2 over the rational number field with big rank. Y.Sumihiro studied the fundamental transformation of vector bundle and the determinant manifold associated to a vector bundle, and proposed a new method of the study of vector bundles on projective spaces.
|
