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arXiv · 2512.08642

Linearity and virtual poly-freeness of the fundamental group of plane curves of degree at most five

Shengkui Ye·Kejia Zhu
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Abstract

We prove that for any algebraic plane curve $C$ of degree at most $5$, the fundamental group $\pi_1(\mathbb CP^2\setminus C)$ is linear and virtually polyfree. As a consequence, we answer positively the open question on the residual finiteness of these groups for all plane curves of degree at most $5$.

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Shengkui Ye, Kejia Zhu. 2025-12-09. Linearity and virtual poly-freeness of the fundamental group of plane curves of degree at most five. https://arxiv.org/abs/2512.08642

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