Counting singular plane curves via Hilbert schemes

被引：5
|
作者：
Russell, H [1 ]
机构：
[1] Oklahoma State Univ, Dept Math, Stillwater, OK 74078 USA
来源：
ADVANCES IN MATHEMATICS | 2003年 / 179卷 / 01期
关键词：
Hilbert scheme; singularities;
D O I：
10.1016/S0001-8708(02)00026-9
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We give a method of counting the number of curves with a given type of singularity in a suitably ample linear series on a smooth surface using punctual Hilbert schemes. The types of singularities for which our results suffice include the topological type with local equation x(a) + y(b) with less than or equal toaless than or equal to3b. We work out the example of curves with the analytic type of singularity with local equation x(2) + y(n) for 1 < n < 9. (C) 2002 Elsevier Science (USA). All rights reserved.
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收藏
页码：38 / 58
页数：21
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