2020 Fiscal Year Final Research Report
Structure of certain normal algebraic surfaces
| Project/Area Number |
18K03240
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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 | Kyoto University |
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Principal Investigator |
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| Project Period (FY) |
2018-04-01 – 2021-03-31
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| Keywords | 代数幾何 / 代数曲面 / 自己正則写像 |
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| Outline of Final Research Achievements |
Our purpose is to study (A) the structure of normal projective surfaces admitting surjective non-isomorphic endomorphisms and (B) defining equations of normal quartic surfaces admitting irrational singular points.
On (A), by resolving an unsolved problem, I have determined the structure of such surfaces except for log del Pezzo surfaces of Picard number 1. On the other hand, I had few opportunities to study (B).
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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 |
代数多様体の全射自己正則写像については, 力学系, 数論, 代数幾何の立場から様々な研究が行われているが, 近年盛んになってきた. 主には同型写像を扱うものが多いが, 非同型な場合も偏極を保つ自己正則写像の場合に極小モデルや有理点について議論しているものも多数ある. 今回の非同型な全射正則写像を持つ正規曲面の場合の分類結果は, 非常に具体的であり, これらの研究に応用されることが多いに期待される.
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