Irreducibility of the Hilbert scheme of smooth curves in P4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {P}
Irreducibility of the Hilbert scheme of smooth curves in P4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {P}
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P4documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage 中平滑曲线希尔伯特方案的不可约性
DOI：
10.1007/s00013-017-1083-7
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发表时间：
2017
影响因子：
0.6
通讯作者：
Yun
中科院分区：
文献类型：
--
作者：
C. Keem;Yun
我们用光滑曲线的Hilbert格式表示，它是其一般点对应于阶和格数为的光滑不可约非退化曲线的分量的并集。在本文中，我们证明了任何非空的是不可约的，一般光滑的，并有期望的维数没有任何限制的genusg。我们的结果增强了Iliev（Proc Am Math Soc 134：2823-2832，2006）早期获得的不可约化结果，其中几个低genuscases未经处理。
We denote bythe Hilbert scheme of smooth curves, which is the union of components whose general point corresponds to a smooth irreducible and non-degenerate curve of degreedand genusgin. In this note, we show that any non-emptyis irreducible, generically smooth, and has the expected dimensionwithout any restriction on the genusg. Our result augments the irreducibility result obtained earlier by Iliev (Proc Am Math Soc 134:2823–2832, 2006), in which several low genuscases have been left untreated.