Boundedness of Fano varieties
| Project/Area Number |
16K17558
|
|---|
| Research Category |
Grant-in-Aid for Young Scientists (B)
|
| Allocation Type | Multi-year Fund |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | The University of Tokyo |
|---|
Principal Investigator |
Jiang Chen 東京大学, カブリ数物連携宇宙研究機構, 特任研究員 (90772773)
|
|---|
| Project Period (FY) |
2016-04-01 – 2019-03-31
|
| Project Status |
Completed (Fiscal Year 2018)
|
| Budget Amount *help |
¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
|
|---|
| Keywords | Fano varieties / boundedness / K-stability / alpha-invariants / pluri-canonical system / Calabi-Yau varieties / general type / geography problem / Fano varieities / Boundedness / Minimal models / Mori fiber spaces / Singularities |
|---|
| Outline of Final Research Achievements |
The goal of my research project is to study the boundedness of Fano varieties and related topics. According to Minimal Model Program, Fano varieties form a fundamental class in birational geometry. Hence it is very interesting to understand the basic properties of this class, such as boundedness. This is one of the most important and interesting problems in birational algebraic geometry. I am interested in the boundedness of Fano varieties as a family, and also the boundedness of various invariants of Fano varieties. I want to develop both general theory and explicit calculation. Also I use the methods and results in the study of Fano varieties to study varieties of other type. I made two main research achievements: firstly, I proved that K-semistable Fano varieties with volumes bounded from below form a bounded family; secondly, with my collaborators, we established the optimal Noether inequality for most threefolds of general type.
|
| Academic Significance and Societal Importance of the Research Achievements |
K安定性と有界性の両方がファノ多様体の研究の中心的なトピックです。 K安定性はファノ多様体のための良いモジュライ空間を構成するための正しい条件であると期待され、有界性はモジュライの構成に向けた最初のステップです。 K半安定ファノ多様体の有界性に関する私の研究は、これら二つの中心的なトピックを組み合わせたものです。
一方、ネーター不等式は一般型の代数曲面の分類理論において非常に重要です。 我々の結果は、ほとんどの一般型三次元多様体に対して最適なネーター不等式を与え、一般型の三次元多様体の分類理論に役立つことが期待される。 証明で私達はファノ多様体の研究からの多くのアイデアを使用します。
|
Report
(4 results)
Research Products
(19 results)
