Counting rational curves on ${\text{K3}}$ surfaces
Counting rational curves on ${\text{K3}}$ surfaces
复制标题
计算 ${ ext{K3}}$ 曲面上的有理曲线
DOI：
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
A. Beauville
中科院分区：
文献类型：
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作者：
A. Beauville
这些注记的目的是解释Yau和Zaslow[Y-Z]发现的表示K3曲面上有理曲线的个数的显著公式。射影K3曲面属于可数多族(FG)g≥1；FG中的一个曲面允许亏格g的曲线的G维线性系统。对常量的天真计算表明，这样的系统将包含正数量的有理(高度奇异)曲线，比如n(G)。公式是∑
The aim of these notes is to explain the remarkable formula found by Yau and Zaslow [Y-Z] to express the number of rational curves on a K3 surface. Projective K3 surfaces fall into countably many families (Fg)g≥1 ; a surface in Fg admits a gdimensional linear system of curves of genus g . A naive count of constants suggests that such a system will contain a positive number, say n(g) , of rational (highly singular) curves. The formula is∑