Ample vector bundles of small curve genera

被引：14

作者：

Maeda, H ^{[1
]}

机构：

[1] Kyushu Univ, Grad Sch Math, Chuo Ku, Fukuoka 810, Japan

来源：

ARCHIV DER MATHEMATIK | 1998年 / 70卷 / 03期

关键词：

Vector Bundle; Nonnegative Integer; Projective Variety; Curve Genus; Small Curve;

D O I：

10.1007/s000130050190

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let E be a vector bundle of rank n - 1 on a smooth complex projective variety X of dimension n greater than or equal to 3, and let g(X, E) be the curve genus of (X, E) defined by the formula 2g(X, E) - 2 = (K-X + c(1)(E))(c-1)(E), where K-X is the canonical bundle of X. Then it is proved that g(X, E) is a nonnegative integer if E is ample. Moreover,polarized pairs (X, E) with g(X, E) less than or equal to 1 are completely classified.

引用

页码：239 / 243

页数：5

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