RATIONAL CURVES OF DEGREE 11 ON A GENERAL QUINTIC 3-FOLD

被引：13

作者：

Cotterill, Ethan ^{[1
]}

机构：

[1] Univ Nantes, Lab Math Jean Leray, UMR 6629, CNRS, F-44322 Nantes 3, France

来源：

QUARTERLY JOURNAL OF MATHEMATICS | 2012年 / 63卷 / 03期

关键词：

CASTELNUOVO; VARIETIES;

D O I：

10.1093/qmath/har001

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that the incidence scheme of rational curves of degree 11 in quintic 3-folds is irreducible. Irreducibility implies a strong form of the Clemens conjecture in degree 11; namely, on a general quintic F in P-4, there are only finitely many smooth rational curves of degree 11, and each curve C is embedded in F with normal bundle O(-1) circle plus O(-1). Moreover, in degree 11, there are no singular, reduced and irreducible rational curves, nor any reduced, reducible and connected curves with rational components on F.

引用

页码：539 / 568

页数：30