Understanding the structure of affine algebraic varieties and its applications
Project/Area Number |
23740008
|
Research Category |
Grant-in-Aid for Young Scientists (B)
|
Allocation Type | Multi-year Fund |
Research Field |
Algebra
|
Research Institution | Niigata University |
Principal Investigator |
KOJIMA HIDEO 新潟大学, 自然科学系, 教授 (90332824)
|
Project Period (FY) |
2011 – 2013
|
Project Status |
Completed (Fiscal Year 2013)
|
Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2011: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
|
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 / 開代数曲面 |
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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Report
(4 results)
Research Products
(21 results)