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 nonhomeomorphic. In particular, for any d >= 4wefindZariski tuples parametrized by the d-roots of unity up to complex conjugation. As a consequence, for any divisorm of d, m not equal 1, 2, 3, 4, 6, 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.