Triangular curves and cyclotomic Zariski tuples

• Autores: Enrique Artal Bartolo , José Ignacio Cogolludo Agustín , Jorge Martín Morales
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 71, Fasc. 3, 2020, págs. 427-441
• Idioma: inglés
• DOI: 10.1007/s13348-019-00269-y
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• Resumen

  • 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 d\ge 4 we find Zariski \left( \left\lfloor \frac{d}{2}\right\rfloor +1\right)-tuples parametrized by the d-roots of unity up to complex conjugation. As a consequence, for any divisor m of d, m\ne 1,2,3,4,6, we find arithmetic Zariski \frac{\phi (m)}{2}-tuples with coefficients in the corresponding cyclotomic field. These curves have abelian fundamental group and they are distinguished using a linking invariant.

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