Abstract:
It is proved that the commutator subgroup of the fundamental group of the complement of any plane affine irreducible Hurwitz curve (or any plane affine irreducible pseudoholomorphic curve) is finitely presented. It is shown that there is a Hurwitz curve (resp. pseudoholomorphic curve) in $\mathbb{CP}^2$ such that the fundamental group of its complement is non-Hopfian and, therefore, this group is not residually finite. We also prove the existence of an irreducible non-singular algebraic curve $C\subset\mathbb C^2$ and a bidisc $D\subset\mathbb C^2$ such that the fundamental group $\pi_1(D\setminus C)$ is non-Hopfian.
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