2011 Fiscal Year Final Research Report
Research for arithmetic and geometry of algebraic varieties including positive characteristic
| Project/Area Number |
20540044
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Tokyo University of Science (2011)
Hiroshima University (2008-2010) |
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Principal Investigator |
HIROYUKI Ito 東京理科大学, 理工学部, 教授 (60232469)
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| Co-Investigator(Renkei-kenkyūsha) |
HIROKADO Masayuki 広島市立大学, 大学院・情報科学研究科, 講師 (40316138)
SAITO Natsuo 広島市立大学, 大学院・情報科学研究科, 講師 (70382372)
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| Project Period (FY) |
2008 – 2011
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| Keywords | 代数幾何学 / 正標数 / 楕円曲面 / K3曲面 / Calabi-Yau多様体 / 特異点 / Mordell-Weil格子 / 有限体 / 疑似乱数 |
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| Research Abstract |
1) We studied stratifications inside the semi-universal deformations of rational double points, and determined some strata and equisingular loci of them. As a corollary, we gave a definition of canonical singularities in positive characteristic and gave a classification. 2) We characterized and classified elliptic K3 surfaces with p^n torsion sections, and gave a moduli space of such K3 surfaces. As a corollary, we checked the validity of Artin-Shioda conjecture and unirationality conjecture for these cases. 4) We explicitly calculated the resolution of quotient singularities arising from the diagonal wild action to the self-product of some algebraic curves. We also gave interesting sequence of algebraic surfaces of general type. 5) Using an explicit construction of Artin-Schreier towers, we invented the new method for generating pseudo-random numbers, which marked the good evaluations by standard test of pseudo-random number generators.
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Research Products
(17 results)
