The embedding structure, defining ideals and the projective m-normality of projective varieties
Project/Area Number |
26400041
|
Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Algebra
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Research Institution | Yokohama National University |
Principal Investigator |
NOMA ATSUSHI 横浜国立大学, 大学院環境情報研究院, 教授 (90262401)
|
Project Period (FY) |
2014-04-01 – 2017-03-31
|
Project Status |
Completed (Fiscal Year 2016)
|
Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
|
Keywords | 射影多様体 / 射影埋め込み / 線形射影 / 定義方程式 / 斉次イデアル / m-正規性 / カステルヌーボマンフォード正則数 / m正規性 / カステルヌーボ-マンフォード正則数 / 射影埋込み |
Outline of Final Research Achievements |
We studied the relation between the embedding structute of projective varieties and their defining equations. For a projective variety X, a point of the projective space is called a nonbirational center of X if the linear projection from it induces a nonbirational map onto its image. By B(X) and C(X), we denote the set of nonbirational centers outside of X and inside of X respectively. We call B(X) and C(X) Segre locus and inner Segre locus respectively. In this study, first we give a characterization of a projective variety X with nonempty B(X) and C(X). As one of applications of this result, we have improved the result on Castelnuovo-Mumford regularity for smooth X of codimension e and degree d by showing that the regularity is at most e(d-e)+1. Second we show that the Castelnuovo-Mumford regularity of X with 1-dimensional C(X) is at most d-e+1. Moreover, as an application of these studies, we have a result of maximal minors of a matrix with homogeneous linear forms as entries.
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Report
(4 results)
Research Products
(11 results)