Understanding the structure of open algebraic surfaces and normal algebraic surfaces of logarithmic Kodaira dimension one or less
| Project/Area Number |
26400042
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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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| Research Field |
Algebra
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| Research Institution | Niigata University |
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Principal Investigator |
Kojima Hideo 新潟大学, 自然科学系, 教授 (90332824)
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| Co-Investigator(Renkei-kenkyūsha) |
KISHIMOTO Takashi 埼玉大学, 理工学研究科, 准教授 (20372576)
SAITO Natsuo 広島市立大学, 情報科学研究科, 講師 (70382372)
TAKAHASHI Takeshi 新潟大学, 自然科学系, 准教授 (60390431)
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| Research Collaborator |
NAGAMINE Takanori
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | 代数幾何学 / 開代数曲面 / 正規代数曲面 / 対数的小平次元 / 多項式環 / 高階導分 / 正規デルペッゾ曲面 / Qホモロジー射影平面 / 消去問題 |
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| Outline of Final Research Achievements |
I have studied open algebraic surfaces, normal algebraic surfaces and kernels of higher derivations in polynomial rings. I proved that, for an irrational open algebraic surface, its logarithmic Kodaira dimension is non-negative if and only if its logarithmic 12 genus is positive. I studied normal del Pezzo surfaces of Picard rank one with only rational log canonical singularities by using structure theorems on open algebraic surfaces and some results on Q-homology planes and gave partial classification results for those surfaces with one or four singular points. I also gave a sufficient condition for the kernel of a locally finite higher derivations in the polynomial ring in three variables to be a polynomial ring. Furthermore, I applied these results to some problems on affine algebraic varieties.
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Report
(4 results)
Research Products
(18 results)
