2022 Fiscal Year Final Research Report
Classifications of compact complex manifolds admitting non-isomorphic endomorphisms
| Project/Area Number |
20K03518
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 11010:Algebra-related
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| Research Institution | Nara Medical University |
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Principal Investigator |
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| Project Period (FY) |
2020-04-01 – 2023-03-31
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| Keywords | endomorphism / extremal ray / minimal model program / ESP / Atiyah surface |
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| Outline of Final Research Achievements |
Classificatioins of smooto projective 3-folds with negative Kodaira dimension which admit a nonisomorphic \'{e}tale endomorphism f has been done: Such varieties can be classified into 6 types. We show that such a variety has at most finite extremal rays R or R is presereved some power of f^k(k > 0). As a consequence, we can apply the eequivariant minimal model program compatibly with \'{e}tale endomorphisms.
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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 |
非特異３次元射影代数多様体で非同型な自己正則写像を許す類の分類を完全に遂行した点が際立っている。
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