Rational curves and rational singularities

被引：26
|
作者：
Flenner, H
Zaidenberg, M
机构：
[1] Ruhr Univ Bochum, Fak Math, D-44780 Bochum, Germany
[2] Univ Grenoble 1, Inst Fourier, CNRS, UMR 5582, F-38402 St Martin Dheres, France
来源：
MATHEMATISCHE ZEITSCHRIFT | 2003年 / 244卷 / 03期
关键词：
D O I：
10.1007/s00209-003-0497-z
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study rational curves on algebraic varieties, especially on normal affine varieties endowed with a C*-action. For arieties with an isolated singularity, covered by a family of rational curves with a general member not passing through the singular point, we show that this singularity is rational. In particular, this provides an explanation of classical results due to H. A. Schwartz and G. H. Halphen on polynomial solutions of the generalized Fermat equation.
引用
收藏
页码：549 / 575
页数：27
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