Applications of minimal model theory to higher dimensional affine algebraic geometry
Project/Area Number |
24740003
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Research Category |
Grant-in-Aid for Young Scientists (B)
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Allocation Type | Multi-year Fund |
Research Field |
Algebra
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Research Institution | Saitama University |
Principal Investigator |
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Project Period (FY) |
2012-04-01 – 2015-03-31
|
Project Status |
Completed (Fiscal Year 2014)
|
Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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Keywords | 極小モデル理論 / アフィン代数多様体 / ユニポテント代数群作用 / affine ruledness / 極小モデル理論 (フランス) / affine ruledness (フランス) / ユニポテント代数群 (フランス) / del Pezzoファイブレーション / affine-uniruledness / affine-ruledness / 群作用 / log canonical threshold / minimal model program / Fano variety / del Pezzo fibration / log uniruled / France (Dijon) / unipotent group / affine cones / France (Grenoble) |
Outline of Final Research Achievements |
Roughly speaking, algebraic geometry deals with two classes of varieties, so-called, projective varieties and affine algebraic varieties. These two classes behave quite differently. The former one, namely, projective varieties can be analyzed by use of several very useful theories, in particular, minimal model theory,which plays remarkably important role for the study of projective varieties from the viewpoint of the behavior of distinguished rational curves. Whereas, as for the latter one, i.e., for affine algebraic varieties, we do not have so far a useful method to investigate them. One of the main reasons to explain this difficulty lies in an impossibility to take a limit over such varieties. To overcome it, we are trying to embed a given affine variety into a projective one in order to apply above mentioned minimal model theory. Of course, several obstacles occur along this attempt, nevertheless we succeed to obtain some useful results.
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Report
(4 results)
Research Products
(14 results)