2013 Fiscal Year Final Research Report
Understanding the structure of affine algebraic varieties and its applications
| Project/Area Number |
23740008
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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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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| Project Period (FY) |
2011 – 2013
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| Keywords | 代数幾何 / アフィン代数曲面 / 対数的小平次元 / 対数的多重種数 / 正規デルペッゾ曲面 / 多項式環 / 高階導分 |
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| Research Abstract |
I have studied the structure of affine algebraic surfaces. I gave another proof of the classification of the additive group scheme action on the affine plane and proved that the logarithmic 12th genus of the smooth part of a normal affine surface of logarithmic Kodaira dimension 1 is positive. Moreover, by using some recent results on affine algebraic surfaces, I studied curves on a normal projective rational surface whose complements have non-positive Euler characteristic and gave an upper bound for the number of singular points of a normal del Pezzo surface of Picard number 1 with only rational log canonical singularities. I also gave necessary and sufficient conditions for a polynomial in the polynomial ring over a unique factorization domain to be closed.
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