2012 Fiscal Year Final Research Report
Problems on algebraic geometry in positive characteristic
| Project/Area Number |
21740027
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Hiroshima City University |
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Principal Investigator |
SAITO Natsuo 広島市立大学, 情報科学研究科, 講師 (70382372)
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| Project Period (FY) |
2009 – 2012
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| Keywords | 正標数 / 代数多様体 / 特異点 / 変形理論 |
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| Research Abstract |
We study various phenomena peculiar to positive characteristic on algebraic geometry. Especially, we investigated local structure of a three dimensional variety X defined over an algebraically closed field k of characteristic p>0 with at most canonical singularities. Under the assumption that the p>2 and a general hyperplane cut of X has at most rational singularities, we showed that local structure of X in codimension two is well understood in the level of local equations. Consequently, we found that any singularity of such a variety X in codimension two is analytically a product of a rational double point and a nonsingular curve with two exceptions in p=3.
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