论文标题
用$ m $折点计数理性曲线
Counting rational curves with an $m$-fold point
论文作者
论文摘要
我们获得了$ \ Mathbb {cp}^2 $的理性程度$ d $曲线数量的递归公式，该公式通过$ 3D+1-m $ $ $通用点，并且具有$ m $ $倍的单数点。其他作者较早地解决了具有三重点的计数曲线的特殊情况。与他人的多余相交理论方法相反，我们通过考虑Kontsevich的递归公式的家庭版本来获得该公式。已经明确解决了大量低度案例。
We obtain a recursive formula for the number of rational degree $d$ curves in $\mathbb{CP}^2$ that pass through $3d+1-m$ generic points and that have an $m$-fold singular point. The special case of counting curves with a triple point was solved earlier by other authors. We obtain the formula by considering a family version of Kontsevich's recursion formula, in contrast to the excess intersection theoretic approach of others. A large number of low degree cases have been worked out explicitly.
