2012 Fiscal Year Final Research Report
Various problems related to the classification in higher dimensional birational geometry
| Project/Area Number |
20340005
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Kyoto University |
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Principal Investigator |
MORI Shigefumi 京都大学, 数理解析研究所, 教授 (00093328)
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| Co-Investigator(Renkei-kenkyūsha) |
MUKAI Shigeru 京都大学, 数理解析研究所, 教授 (80115641)
NAKAYAMA Noboru 京都大学, 数理解析研究所, 准教授 (10189079)
KAWAKITA Masayuki 京都大学, 数理解析研究所, 准教授 (10378961)
KAWANOUE Hiraku 京都大学, 数理解析研究所, 助教 (50467445)
NAMIKAWA Yoshinori 京都大学, 理学研究科, 教授 (80228080)
FUJINO Osamu 京都大学, 理学研究科, 准教授 (60324711)
TAKAGI Hiromichi 東京大学, 数理科学研究科, 准教授 (30322150)
HAYAKAWA Takayuki 金沢大学, 数物科学系, 講師 (20198823)
SUMIHIRO Hideyasu 広島大学, 大学院・理学研究科, 名誉教授 (60068129)
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| Research Collaborator |
PROKHOROV Yuri モスクワ大学, 教授
MATSUKI Kenji パデュー大学, 教授
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| Project Period (FY) |
2008 – 2012
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| Keywords | Q コニック束 / 因子収縮射 / フリップ収縮射 / 反標準線形系 / Du Val 特異点 / 端末特異点 / 特異点解消 / 極小モデルプログラム |
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| Research Abstract |
We study extremal contraction morphisms of terminal threefolds such that the inverse image F of a point z is an irreducible curve, and try to classify the neighbourhood of F. They consist of 3 kinds, flipping contractions, divisorial contractions, and Q -conic bundles. Among them, flipping contractions had been classified, and we have found that the rest can be studied. There are at most two non-Gorenstein points, and the one-point case has been classified except for one case, and the treatment of the exceptional case is being written. Kawakita has proved that a divisorial contraction such that F is a surface is a weighted blow up. Kawanoue and Matsuki have introduced an invariant for a singular surface embedded in a smooth threefold which effectively improves in a sequence of blow ups specified by their algorithm which resolves the singularity of the surface.
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