关于有理单分支射影平面曲线的自由与近自由猜想

中文摘要 AI 辅助

设$C\subset \PP^2$为一条约化不可约复平面曲线，其补集为$U$。本文证明了$\chi(U)\geq \nu(C)$，其中$\nu(C)$为$C$的自由缺陷，定义见文献\cite{Dim24}。当$C$为具有单分支奇点的有理曲线时，该不等式证明了Dimca和Sticlaru的猜想，即有理单分支平面曲线要么是自由的，要么是近自由的。

英文摘要

Let $C\subset \PP^2$ be a reduced irreducible complex plane curve with complement $U$. In this paper we prove that $χ(U)\geq ν(C)$, where $ν(C)$ is the freeness defect of $C$ defined in \cite{Dim24}. When $C$ is a rational curve with unibranched singularities, this inequality proves the conjecture of Dimca and Sticlaru, that a rational unibranched plane curve is either free or nearly free.

发表机构

• Tongji University（同济大学）

机构由 AI 辅助整理，请以论文原文为准。