2013 Fiscal Year Final Research Report
Castelnuovo-Mumford regularity for projective variety and its related topics
| Project/Area Number |
21540044
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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 | Saga University |
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Principal Investigator |
MIYAZAKI Chikashi 佐賀大学, 工学(系)研究科(研究院), 教授 (90229831)
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| Co-Investigator(Kenkyū-buntansha) |
ICHIKAWA Takashi 佐賀大学, 大学院工学系研究科, 教授 (20201923)
OKADA Takuzo 佐賀大学, 大学院工学系研究科, 教授 (20547012)
TERAI Naoki 佐賀大学, 文化教育学部, 教授 (90259862)
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| Co-Investigator(Renkei-kenkyūsha) |
NOMA Atsushi 横浜国立大学, 大学院環境情報学研究院, 教授 (90262401)
AMASAKI Mutsumi 広島大学, 大学院教育学研究科, 准教授 (10243536)
OGATA Shoetsu 東北大学, 大学院理学研究科, 准教授 (90177113)
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| Project Period (FY) |
2009-04-01 – 2014-03-31
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| Keywords | 代数幾何 / 可換環論 / 射影多様体 / 多項式イデアル / 極小自由分解 / シジジー / Castelnuovo-Mumford |
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| Research Abstract |
The minimal free resolution of a projective variety is one of the most important algebraic invariants measuring the complexity of the defining ideal of the variety. My research focuses on bounding the Castelnuovo-Mumford regularity introduced by Mumford. Upper bounds on the regularity of Buchsbaum varieties is known to be described in terms of the degree and the codimension of the variety. I have obtained that a Buchsbaum variety with extremal and next-extremal case having Castelnuovo-type regularity bound is a divisor on either a variety of minimal degree or Del Pezzo variety. Also I have obtained a Horrocks-type criterion on the splitting of vector bundles on multiprojective space as an application of Castelnuovo-Mumford regularity.
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