论文标题
在平面曲线节点的位置
On the position of nodes of plane curves
论文作者
论文摘要
给定度量$ d $的平面曲线的Severi品种$ v_ {d，n} $ and $ n $ nodes允许希尔伯特方案的地图$ \ mathbb {p}^{2 [n]} $的零二维子处理的$ \ mathbb {p}^2 $ $ n $ n $ n $ n $ n $ n $ n $。该地图分配给V_ {d，n} $的每个曲线$ c \其节点。对于大约$ n $，我们考虑了这张图的图像，这些图像及其部分的压实。我们在pic $（\ mathbb {p}^{2 [n]}）$中计算此类图像的除数类，并提供枚举数字的节点曲线。我们还直接回答了Diaz-Harris的问题，即Severi品种的规范类别是否有效。
The Severi variety $V_{d,n}$ of plane curves of a given degree $d$ and exactly $n$ nodes admits a map to the Hilbert scheme $\mathbb{P}^{2[n]}$ of zero-dimensional subschemes of $\mathbb{P}^2$ of degree $n$. This map assigns to every curve $C\in V_{d,n}$ its nodes. For some $n$, we consider the image under this map of many known divisors of the Severi variety and its partial compactification. We compute the divisor classes of such images in Pic$(\mathbb{P}^{2[n]})$ and provide enumerative numbers of nodal curves. We also answer directly a question of Diaz-Harris about whether the canonical class of the Severi variety is effective.
