| Project/Area Number |
09440012
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Osaka University |
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Principal Investigator |
MIYANISHI Masayoshi Graduate School of Science, Osaka University, Professor, 大学院・理学研究科, 教授 (80025311)
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| Co-Investigator(Kenkyū-buntansha) |
NAMIKAWA Yoshinori Graduate School of Science, Osaka University, Associate Professor, 大学院・理学研究科, 助教授 (80228080)
FUJIKI Akira Graduate School of Science, Osaka University, Professor, 大学院・理学研究科, 教授 (80027383)
HIBI Takayuki Graduate School of Science, Osaka University, Professor, 大学院・理学研究科, 教授 (80181113)
OHNO Koji Graduate School of Science, Osaka University, Assistant, 大学院・理学研究科, 助手 (20252570)
HIRACHI Kengo Graduate School of Science, Osaka University, Assistant Professor, 大学院・理学研究科, 講師 (60218790)
後藤 竜司 大阪大学, 大学院・理学研究科, 講師 (30252571)
小谷 眞一 大阪大学, 大学院・理学研究科, 教授 (10025463)
佐竹 郁夫 大阪大学, 大学院・理学研究科, 助手 (80243161)
村上 順 大阪大学, 大学院・理学研究科, 助教授 (90157751)
鈴木 昌和 九州大学, 大学院・数理学研究科, 教授 (20112302)
増田 佳代 姫路工業大学, 理学部, 講師 (40280416)
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| Project Period (FY) |
1997 – 1999
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| Project Status |
Completed (Fiscal Year 1999)
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| Budget Amount *help |
¥15,200,000 (Direct Cost: ¥15,200,000)
Fiscal Year 1999: ¥3,700,000 (Direct Cost: ¥3,700,000)
Fiscal Year 1998: ¥3,800,000 (Direct Cost: ¥3,800,000)
Fiscal Year 1997: ¥7,700,000 (Direct Cost: ¥7,700,000)
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| Keywords | Algebraic variety / Affine space / Jacobian Conjecture / Homology plane / Finite graph / Twistor space / Calabi-Yau manifold / topological invariant / 開代数曲面 / 群作用 / 組み合わせ論 / 自己同型写像 / 3次元多様体 / 平面アフィン曲線 / 次数最小埋め込み / 不変式 / 有限生成性 / アルゴリズム / Kontsevich不変量 / 強擬凸領域 |
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| Research Abstract |
1. The head investigator, Masayoshi Miyanishi, investigated jointly with Kayo Masuda, an automorphism of infinite order of the affine space such that the automorpism fixes pointwise a subvariety and that the codimension of the subvariety is small. As a by-product, they obtained an algebro-geometric characterization of the affine 3-space in terms of GィイD2mィエD2-actions. The head investigator also worked out, jointly with R.V.Gurjar of the Tata Institute, a generalization of the Jacobian Conjecture to the Q-homology planes and proved that the conjecture holds true if the logarihmic Kodaira dimension is l and in the most cases if the logarithmic Kodaira dimension is 0 or -∞. A major work of the head investigator during this period of research under the above title is to have written down a book on open algebraic surfaces which is to be published from the American Mathematical Society.
2. Takayuki Hibi investigate finite graphs via the algebras associated to such graphs and the ideals of the
… More
algebras. Study of the Betti numbers of the algebras associated to various simplical complexes provides us with abundant imformations and has become an effective tool which combines combinatorics, commutative algebras and algebraic geometry.
3. Akira Fujiki obtained interesting results via an investigation of algebraic reduction of the twistor spaces on Hopf surfaces. Twistor space is a notion which is close to projective space bundle and expected to clarify differences between algebraic varieties and complex manifolds.
4. Yoshinori Namikawa investigated Calabi-Yau manifolds via deformation theory. He also reconstructed flops via deformation theory which appear in the study of birational mappings of higher dimensional algebraic varieties.
5. Jun Murakami constructed a new invariant for three-dimensional manifolds which is based on the Kontsevich invariant for the knots and studied its properties. He constructed a topological quantum theory by making use of this invariant, and a family of mapping groups of surfaces as its application.
6. Koji Yanagawa made a joint research with E.Ballico on h-vectors of the Poincare series which are defined by Cohen-Macaulay domains over a field of characteristic ρ. Less
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