Deformation and classification of Fano varieties and Calabi-Yau varieties
| Project/Area Number |
16K17573
|
|---|
| Research Category |
Grant-in-Aid for Young Scientists (B)
|
| Allocation Type | Multi-year Fund |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | Kobe University |
|---|
Principal Investigator |
Sano Taro 神戸大学, 理学研究科, 助教 (10773195)
|
|---|
| Project Period (FY) |
2016-04-01 – 2020-03-31
|
| Project Status |
Completed (Fiscal Year 2019)
|
| Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
|
|---|
| Keywords | Fano多様体 / Calabi-Yau多様体 / 変形理論 / 代数幾何学 / 曲線のモジュライ空間 / 代数学 |
|---|
| Outline of Final Research Achievements |
I studied several problems on Fano varieties and Calabi-Yau varieties which form building blocks in the classification theory. With Pizzato and Tasin, we solved the effective non-vanishing conjecture on weighted complete intersections. With Coughlan, we showed that many affine cones over K3 surfaces or Abelian varieties do not admit smoothings. With Okawa, we showed the non-commutative rigidity of the moduli stack of stable pointed curves except for finitely many cases. With Hashimoto, we constructed examples of non-Kahler Calabi-Yau 3-folds with arbitrarily large 2nd Betti numbers.
|
| Academic Significance and Societal Importance of the Research Achievements |
代数多様体の分類理論は代数幾何学における中心的な話題であり、その核となるFano多様体、Calabi-Yau多様体の分類を進めるのは意義がある。また、最近はFano多様体に関連する研究の進展は目覚ましく、注目度は高い。Calabi-Yau多様体に関連する研究はFano多様体に比べると小康状態であるが、次に目覚ましい進展が訪れる可能性があり、アイデアを積み重ねる価値がある分野と思う。
|
Report
(5 results)
Research Products
(29 results)
