2020 Fiscal Year Final Research Report
Characterization of homogeneous varieties by means of tangent bundles
| Project/Area Number |
17K14153
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Chuo University (2020)
Saitama University (2017-2019) |
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Principal Investigator |
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| Project Period (FY) |
2017-04-01 – 2021-03-31
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| Keywords | 接束 / ネフ / 等質多様体 / 有理曲線 / ファノ多様体 / 有理連結多様体 |
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| Outline of Final Research Achievements |
I studied projective varieties from the viewpoint of the positivity of the tangent bundle. I wrote three papers on the Campana-Peternell conjecture "Any Fano manifold with nef tangent bundle is homogeneous". I also studied more wide class of varieties. As a consequence, I obtained a structure theorem of varieties with nef second exterior power of the tangent bundle and a positive characteristic analogue of the Demailly-Peternell-Scheneider theorem.
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| Free Research Field |
代数幾何学
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| Academic Significance and Societal Importance of the Research Achievements |
４年間の研究期間のうちに，5本の論文を執筆し，うち4本が出版された．とりわけ，研究課題であるカンパーナ・ペターネル予想（以下CP予想）に関連し，F4(4)型の等質多様体の特徴付けを得た．また，余指数3のファノ多様体に対してCP予想を肯定的に解決した．CP予想の解決には届かなかったが，その一方で，接束の二階外積がネフである多様体の構造定理と正標数の体上定義されたネフ接束を持つ射影多様体の構造定理を得た．CP予想より広い枠組みで構造定理を得ることができたことで，今後の研究に広がりができた．
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