Computation-free presentation of the fundamental group of generic $(p,q)$-torus curves

Mathematics – Algebraic Geometry

Scientific paper

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7 pages, 3 figures

Scientific paper

In this note, we present a new method for computing fundamental groups of
curve complements using a variation of the Zariski-Van Kampen method on general
ruled surfaces. As an application we give an alternative (computation-free)
proof for the fundamental group of generic $(p,q)$-torus curves.

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