Grant-in-Aid for Scientific Research (B)
|Allocation Type||Single-year Grants |
|Research Institution||Osaka University |
KONNO Kazuhiro Osaka University, Graduate School of Scence, Professor (10186869)
USUI Sampei Osaka University, Graduate School of Science, Professor (90117002)
ENDO Hisaaki Osaka University, Graduate School of Science, Associate Professor (20323777)
ASHIKAGA Tadashi Tohtoku Gakain University, Facultyof Engineering, Professor (90125203)
TOKUNAGA Hiro-o Tokyo Metrophtan University, Graduate School of Science, Professor (30211395)
SHIMADA Ichiro Hokkaido University, Graduate School of Saence, Associate Professor (10235616)
難波 誠 追手門学院大学, 経済学部, 教授 (60004462)
吉原 久夫 新潟大学, 自然科学系, 教授 (60114807)
中山 昇 京都大学, 数理解析研究所, 助教授 (10189079)
|Project Period (FY)
2004 – 2007
Completed (Fiscal Year 2007)
|Budget Amount *help
¥14,780,000 (Direct Cost: ¥13,700,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2007: ¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2006: ¥3,100,000 (Direct Cost: ¥3,100,000)
Fiscal Year 2005: ¥3,100,000 (Direct Cost: ¥3,100,000)
Fiscal Year 2004: ¥3,900,000 (Direct Cost: ¥3,900,000)
|Keywords||Pencil of algebraic curves / local signature / branched covering / Mordell-Weil lattice / Galois point / Zanski pair / 標準サイクル / スロープ / ガロワ点 / 退化 / 局所不変量 / K3曲面 / 標準線形系 / endomorphism / 有理曲面 / Mordell-Weil lattice / fibration / モジュライ / ガロア被覆 / 符号数 / モノドロミー / コンパクト化 / 超特異K3局面|
The purpose of the research project is to study pencils of algebraic curves from mainly two sides. One is algebraic geometry and the other is topology. The interaction between two fields of mathematics has been crucial .We paid our special attention to the following topics.
(1) The slope of fibred algebraic surfaces,
(2) The localization of signature,
(3) The Mordell-Weil lattices.
Our achievements include: the lower bounds of the slopes for fibred rational surfaces, the inequality involving the Clifford index of a general fibre and the Mordell Weil rank, the complete description of fibred rational surfaces with extremal Mordell-Weil rank, the rationality or ellipticity of the singularity obtained by contracting the fixed part of the relative canonial linear system for a normal surface singularity and a fibred algebraic surface, the comparison between local signatures obtained from the eta invariant and semi-stable reduction of a singular fibre germ. During the research period, in total, 57 papers are written and 121 research presentations are given by our investigators. We organized (or co-organized) 6 conferences. Above all, we held the international conference "Algebraic Geometry in East Asia, II" at Hanoi(Vietnam), October 2005, in order to promote research interaction among algebraic geometers in the area. We published the proceedings of the meetings to show the activity of the research project. Also, we invited 6 researchers in abroad and discussed verious problems fruitfully.
In sum, our purpose has been achieved m great success, thanks to the active contributions and cooperation of our joint investigators.