Study of complex analytic maps, Vojta's conjecture and invariants
| Project/Area Number |
15K04917
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Basic analysis
|
|---|
| Research Institution | The University of Tokyo |
|---|
Principal Investigator |
Noguchi Junjiro 東京大学, 大学院数理科学研究科, 名誉教授 (20033920)
|
|---|
| Research Collaborator |
Yamanoi Katsutoshi
Ohsawa Takeo
Takayama Shigeharu
Tsuji Hajime
Hirata Noriko (Kohno Noriko)
Hamano Sachiko
|
|---|
| Project Period (FY) |
2015-04-01 – 2019-03-31
|
| Project Status |
Completed (Fiscal Year 2018)
|
| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2018: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
|
|---|
| Keywords | 解析学 / 関数論 / 多変数複素解析学 / 値分布理論 / Vjota予想 / Vojta予想 |
|---|
| Outline of Final Research Achievements |
(1) In the study of the value distribution theory and Vojta Conjecture, I gave another proof of M. Raynaud's Theorem (1983) by making use of Big Picard's Theorem for semi-abelian vareities by the author (1981) combined with ``o-minimal structure''. This provides a first instance of a direct relation at proof level between them, whereas the analogies at statement level have been discussed a lot.
(2) Some sufficient condition for the Levi (Hatogs' Inverse) Problem to hold was firstly given, and as well another proof of Behnke-Stein's Theorem (the Steinness of open Riemann sufaces) was given. I improved the algorithmical structure of the proof of Oka's Coherence Theorem, and then obtained a ``Weak Coherence Theorem'': It makes possible to provide a complete self-contained treatment of the solutions of the Three Big Problems (Behnke-Thullen, 1934) due to K. Oka (1936-1953) in a very elementary way only with convergent power series and Cousin's integral (half of Cauchy's integral).
|
| Academic Significance and Societal Importance of the Research Achievements |
多変数複素解析学における値分布理論と代数多様体上の有理点分布の理論は、これまで命題文レベルでのアナロジーとして研究されてきた．今回，成果としてそれ等両者の間に証明レベルでの直接的な関係を見出した．間を取りもたったのがロッジックのモデル理論である「極小順序構造・集合」の理論であるこが，興味深い。
多変数複素解析学においてレビ(ハルトークスの逆)問題は基本的である．不分岐領域の場合は岡により解決され，分岐の場合は反例があることが知られているが、ここでは初めて成立の為の十分条件が与えられた。弱連接定理を定式化することにより，岡による三大問題の解決に限ればごく初等的な証明が可能であることを示した。
|
Report
(5 results)
Research Products
(109 results)
