2010 Fiscal Year Final Research Report
Extensions and applications of the theory of toric varieties
| Project/Area Number |
19340001
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 | Tohoku University |
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Principal Investigator |
ISHIDA Masanori 東北大学, 大学院・理学研究科, 教授 (30124548)
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| Co-Investigator(Kenkyū-buntansha) |
OGATA Shoetsu 東北大学, 大学院・理学研究科, 准教授 (90177113)
YUKIE Akihiko 東北大学, 大学院・理学研究科, 教授 (20312548)
HANAMURA Masaki 東北大学, 大学院・理学研究科, 教授 (60189587)
HARA Nobuo 東北大学, 大学院・理学研究科, 准教授 (90298167)
KAJIWARA Takeshi 横浜国立大学, 大学院・工学研究院, 准教授 (00250663)
ASHIKAGA Tadashi 東北学院大学, 工学部, 教授 (90125203)
TSUCHIHASHI Hiroyasu 東北学院大学, 教養学部, 教授 (00146119)
TAKAHASHI Tomokuni 一関工業高等専門学校, 准教授 (50259793)
SATO Hiroshi 岐阜聖徳学園大学, 経済情報学部, 准教授 (20433310)
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| Project Period (FY) |
2007 – 2010
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| Keywords | トーリック多様体 / 扇 / 凸多面体 / 循環商特異点 / 代数多様体 |
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| Research Abstract |
We have studied on the extensions and applications of the theory of toric varieties. We got new results on the extensions of the concepts of fans and semigroup rings and associated toric varieties and their extensions, locally finite scheme associated to a decomposition of a real space by not necessarily bounded polytopes. We also got results on the Minkowskii sums of convex polytopes and very ampleness and normality of line bundles, normal varieties factoring Frobenius morphisms, and resolutions of higherdimensional cyclic quotient singularities.
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