Deformations of curves on a higher dimensional algebraic variety and their obstructions

高维代数簇上曲线的变形及其阻碍

• 批准号: 21740029
• 负责人: NASU Hirokazu
• 金额: $ 1.08万
• 依托单位: Tokyo Denki University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2010
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21740029/
• 关键词: ヒルベルトスキーム; 変形理論; 空間曲線; 無限小変形; 障害; 代数多様体; スクロール; リエゾン; 非被約成分; 障害類; デルペッツォ多様体

In this project, we investigated infinitesimal deformations of curves on a higher dimensional algebraic variety and their obstructions, and non-reduced components of the Hilbert scheme. As a result, we have proved a conjecture due to Kleppe and Ellia, which is concerned with non-reduced components of the Hilbert scheme of space curves, in the case where a general member of the components are quadratically normal. We also study the deformations of degenerate curves on a higher dimensional scroll, and construct a family of curves, which have a first order deformation not liftable to the second order deformation.

在这个项目中，我们研究了高维代数簇上曲线的无穷小变形及其障碍，以及希尔伯特格式的非约化分量。因此，我们证明了Kleppe和Ellia的一个猜想，该猜想涉及空间曲线的Hilbert概型的非约化分量，其中一般分量是二次正规的.我们还研究了高维涡卷上退化曲线的变形，构造了一类曲线族，它们的一阶变形不能提升到二阶变形。

项目成果

Obstructions to deforming space curves and a remark to a conjecture of Kleppe (in Japanese)

空间曲线变形的障碍及对 Kleppe 猜想的评述（日文）

• 发表时间: 2009
• 期刊: 研究集会「射影多様体の幾何とその周辺2009」報告集
• 作者: Ei Kobayashi;Shigeru Kuroda;Shigeru Kuroda;Shigeru Kuroda;黒田茂;Shigeru Kuroda;Shigeru Kuroda;Shigeru Kuroda;Shigeru Kuroda;Shigeru Kuroda;Shigeru Kuroda;Shigeru Kuroda;Shigeru Kuroda;Shigeru Kuroda;Shigeru Kuroda;Shigeru Kuroda;那須弘和;那須弘和
• 通讯作者: 那須弘和

Obstructions to deforming degenerate curves on a scroll (in Japanese)

阻碍卷轴上退化曲线变形（日语）

• 发表时间: 2010
• 期刊: 研究集会「都の西北代数幾何学シンポジウム」報告集
• 作者: Ei Kobayashi;Shigeru Kuroda;Shigeru Kuroda;Shigeru Kuroda;黒田茂;Shigeru Kuroda;Shigeru Kuroda;Shigeru Kuroda;Shigeru Kuroda;Shigeru Kuroda;Shigeru Kuroda;Shigeru Kuroda;Shigeru Kuroda;Shigeru Kuroda;Shigeru Kuroda;Shigeru Kuroda;那須弘和
• 通讯作者: 那須弘和

Obstructions to deforming curves on a 3-fold, I-a generalization of Mumford's example and an application to Hom schemes-

3 倍变形曲线的障碍，I-Mumford 示例的推广以及 Hom 方案的应用-

• 期刊: J. Alg. Geom. (to appear掲載確定)
• 作者: S. Mukai;H. Nasu
• 通讯作者: H. Nasu

Obstructions to deforming degenerate curves on a scroll

阻碍滚动上简并曲线变形

• 发表时间: 2011
• 作者: 向井茂;那須弘和;那須弘和
• 通讯作者: 那須弘和

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