On Chow stability for algebraic curves

详细信息    查看全文

• 作者：L. Brambila-Paz ; H. Torres-López
• 关键词：Mathematics Subject Classification14H60 ; 14H10 ; 14C05 ; 14D23
• 刊名：manuscripta mathematica
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：151
• 期：3-4
• 页码：289-304
• 全文大小：478 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Algebraic Geometry
  Topological Groups and Lie Groups
  Geometry
  Number Theory
  Calculus of Variations and Optimal Control
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-1785
• 卷排序：151

文摘

In the last decades there have been introduced different concepts of stability for projective varieties. In this paper we give a natural and intrinsic criterion for the Chow and Hilbert stability for complex irreducible smooth projective curves \(C\subset {\mathbb {P}} ^n\). Namely, if the restriction of the tangent bundle of \({\mathbb {P}} ^n\) to C is stable then \(C\subset {\mathbb {P}} ^n\) is Chow stable, and hence Hilbert stable. We apply this criterion to describe a smooth open set of a regular component of the locus of Chow stable curves of the Hilbert scheme of \(\mathbb {P} ^n\) with Hilbert polynomial \(P(t)=dt+(1-g)\), when \(g\ge 4\) and \(d>g+n-\left\lfloor \frac{g}{n+1}\right\rfloor .\) Moreover, we describe the quotient stack of such curves. Similar results are obtained for the locus of Hilbert stable curves.