2010 Fiscal Year Final Research Report
Defining ideals of projective varieities and their embedding structure
| Project/Area Number |
20540039
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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 | Yokohama National University |
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Principal Investigator |
NOMA Atsushi Yokohama National University, 教育人間科学部, 准教授 (90262401)
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| Project Period (FY) |
2008 – 2010
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| Keywords | 射影多様体 / 射影空間への埋め込み / 線形射影 / 内点射影 / 定義方程式 / 斉次イデアル / カステルヌーボーマンフォード正則性 / 二重点因子 |
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| Research Abstract |
For a projective variety, a point from which the variety is projected nonbirationaly onto its image is called a nonbirational center. In this research, we obtained a characterization of projective varieties with nonbirational center(s). As applications of this characterization, for a smooth projective variety, we showed some semiampleness of its ideal sheaf and improved the regularity bound of the ideal sheaf. On the other hand, as an application of linear projections, we show the very ampleness of the double-point divisor of a projective variety.
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