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arXiv · 2609.24810

On Free and Nearly Free Conjecture of Rational Unibranched Projective Plane Curves

Xiping Zhang
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Abstract

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.

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Xiping Zhang. 2026-09-21. On Free and Nearly Free Conjecture of Rational Unibranched Projective Plane Curves. https://arxiv.org/abs/2609.24810

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