Irreducibility of the (-1)-classes on smooth rational surfaces

被引：5

作者：

Lahyane, M ^{[1
]}

机构：

[1] Abdus Salam Int Ctr Theoret Phys, I-34100 Trieste, Italy

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2005年 / 133卷 / 08期

关键词：

smooth rational surfaces; anticanonical divisor; Hodge Index Theorem; points in general position; Neron-Severi group; blowing-up;

D O I：

10.1090/S0002-9939-05-07654-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We give a characterization for a (-1)-divisor D on a smooth rational surface X to be irreducible under the assumption that an anticanonical divisor -K-X of X is nef. Here -K-X is nef means K-X.C ≤ 0 for every effective divisor C on X, and a (-1)-divisor D is a divisor such that the two numerical conditions D-2 = -1 = D.K-X hold. As an application we give explicit examples of blowing up the projective plane at nine points infinitely near such that the obtained surface has an infinite number of (-1)-curves. A (-1)-curve is a smooth rational curve of self-intersection -1.

引用

页码：2219 / 2224

页数：6