2023 Fiscal Year Final Research Report
Local-global correspondance in birational geometry
| Project/Area Number |
18H01108
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (B)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Review Section |
Basic Section 11010:Algebra-related
|
|---|
| Research Institution | The University of Tokyo |
|---|
Principal Investigator |
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
中村 勇哉 東京大学, 大学院数理科学研究科, 助教 (20780034)
|
|---|
| Project Period (FY) |
2018-04-01 – 2023-03-31
|
| Keywords | MMP |
|---|
| Outline of Final Research Achievements |
I have published a paper with Yusuke Nakamura and Wei-chung Chen on the generalized minimal log discrepancies. This paper has been published in JMSJ. A further development is the study of the Mukai-type conjecture from the perspective of local-global correspondence. I have introduced a new invariant of total exponent for Fano manifolds and have studied the characterization of the projective space of the Mukai-type conjecture. I have been able to prove that the conjecture holds if we assume the Ambro-Kawamata effective non-vanishing conjecture holds, so the conjecture itself seems to be correct. The paper including the above results are will be published by Kyoto Math. Journal. I have also investigated the case of curved surfaces in more detail in collaboration with Moraga.
|
| Free Research Field |
代数幾何学
|
| Academic Significance and Societal Importance of the Research Achievements |
研究成果の学術的意味は、オリジナルの向井予想への新しいアプローチを考えられたので十分意義があったと思う。さらにその視点からショクロフ学派の数学が有用であることを示唆しているので、その方向からのアプローチがMoragaらを中心に活性化させることができたので十分意味があったと思う。
|
