Defining ideals of projective varieities and their embedding structure

定义射影簇的理想及其嵌入结构

• 批准号: 20540039
• 负责人: NOMA Atsushi
• 金额: $ 2.83万
• 依托单位: Yokohama National University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2008
• 资助国家: 日本
• 起止时间: 2008 至 2010
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20540039/
• 关键词: 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; projective variety; projective embedding; linear projection; double point divisor; inner projection; Castelnuovo-Mumford regularity; defining equation; hypersurface; h

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.

对于投影簇，将簇非无理地投影到其图像上的点称为非无理中心。在这项研究中，我们获得了具有非双理性中心的投射簇的表征。作为这种表征的应用，对于平滑射影簇，我们展示了其理想层的一些半充足性，并改进了理想层的正则性界限。另一方面，作为线性投影的应用，我们展示了投影簇的双点除数的丰富性。

项目成果

Multisecant subspaces to smooth projective varieties in arbitrary characteristic

多重割线子空间可平滑任意特征的射影簇

• 发表时间: 2009
• 期刊: Proceedings of the American Mathemtical Society Vol.137(12)
• 作者: H.Abe;M.Hoshino;Yasuo Ohno;Atsushi Noma;小木曽岳義;Yasuo Ohno;Atsushi Noma
• 通讯作者: Atsushi Noma

Structure of projective varieties with non-birational linear projections and its applications

非双有理线性投影射影簇的结构及其应用

• 发表时间: 2009
• 作者: 佐藤文広;小木曽岳義;Atsushi NOMA;小木曽岳義;Atsushi Noma;小木曽岳義;Atsushi Noma;Atsushi Noma;小木曽岳義;Atsushi Noma;Atsushi Noma;Atsushi Noma;Atsushi Noma;Atsushi Noma
• 通讯作者: Atsushi Noma

Hyper surfaces cutting out a projective variety

超曲面切割射影变化

• 发表时间: 2008
• 作者: 佐藤文広;小木曽岳義;Atsushi NOMA;小木曽岳義;Atsushi Noma;小木曽岳義;Atsushi Noma;Atsushi Noma;小木曽岳義;Atsushi Noma;Atsushi Noma;Atsushi Noma;Atsushi Noma;Atsushi Noma;Atsushi Noma;浅沼照雄;Atsushi Noma;浅沼照雄;Atsushi Noma;Atushi Noma;Atsushi NOMA;Atsushi Noma;Atsushi NOMA;浅沼照雄;Atsushi Noma;Atsushi NOMA
• 通讯作者: Atsushi NOMA

Projective varieties with nonbirational linear projection

具有非无理线性投影的投影簇

• 发表时间: 2009
• 作者: 佐藤文広;小木曽岳義;Atsushi NOMA;小木曽岳義;Atsushi Noma;小木曽岳義;Atsushi Noma;Atsushi Noma;小木曽岳義;Atsushi Noma;Atsushi Noma;Atsushi Noma;Atsushi Noma;Atsushi Noma;Atsushi Noma;浅沼照雄;Atsushi Noma;浅沼照雄;Atsushi Noma;Atushi Noma
• 通讯作者: Atushi Noma

Generic inner projections of projective varieties and an application to the positivity of double-point divisors

射影簇的一般内投影及其在双点除数正性中的应用

• 发表时间: 2010
• 作者: 佐藤文広;小木曽岳義;Atsushi NOMA;小木曽岳義;Atsushi Noma;小木曽岳義;Atsushi Noma;Atsushi Noma
• 通讯作者: Atsushi Noma