2013 Fiscal Year Final Research Report
The embedding structure of projective varieties and their defining ideals
| Project/Area Number |
23540043
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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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 横浜国立大学, 環境情報研究院, 教授 (90262401)
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| Project Period (FY) |
2011 – 2013
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| Keywords | 射影多様体 / 射影埋込み / 線形射影 / 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数 |
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| Research Abstract |
Let X be an n-dimensional projective variety of degree d and codimension e. A point is called nonbirational center of X if the linear projection from the point induces nonbirational map to the image. By B(X) and C(X) we denote the set of nonbirational center outside of X and inside of X, respectively. In this study, first, for smooth X having C(X) of dimension at least 1, we show that X is (d-e+1)-regular in most cases. Second we show that if C(X) is a point and if the image of the linear projection from the point is rational scroll, the double point divisor of X is base-point-free. Third we give an construction of an example of X whose B(X) has two irreducible components of dimension at least one.
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