393 research outputs found
Triangular curves and cyclotomic Zariski tuples
The purpose of this paper is to exhibit infinite families of conjugate
projective curves in a number field whose complement have the same abelian
fundamental group, but are non-homeomorphic. In particular, for any we
find Zariski tuples parametrized by the -roots of unity up to complex
conjugation. As a consequence, for any divisor of , ,
we find arithmetic Zariski -tuples with coefficients in the
corresponding cyclotomic field. These curves have abelian fundamental group and
they are distinguished using a linking invariant.Comment: 15 pages, 3 figures. To appear in Collectanea Mathematic
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