170400 20260420103354.0 doi 10.1007/s13398-026-01853-1 sideral 148905 ART-2026-148905 eng Cogolludo-Agustín, José I. Universidad de Zaragoza (orcid)0000-0003-1820-6755 On the topology of fiber-type curves: an affine Zariski pair of nodal curves 2026 In this paper we explore conditions for a curve in a smooth projective surface to have a free product of cyclic groups as the fundamental group of its complement. It is known that if the surface is P2, then such curves must be of fiber type, i.e. a finite union of fibers of an admissible map onto a complex curve. In this setting, we exhibit an infinite family of Zariski pairs of fiber-type curves, that is, pairs of plane projective fiber-type curves whose tubular neighborhoods are homeomorphic, but whose embeddings in P2 are not. This includes a Zariski pair of curves in C2 with only nodes as singularities (and the same singularities at infinity) whose complements have non-isomorphic fundamental groups, one of them being free. Our examples show that the position of nodes also affects the topology of the embedding of projective curves. Twisted Alexander polynomials with respect to finite SU(2) representations show to be useful for this purpose, since all their abelian invariants are the same for both fundamental groups. Access copy available to the general public Unrestricted info:eu-repo/grantAgreement/ES/DGA/E22-20R info:eu-repo/grantAgreement/ES/MCIU/PID2024-156181NB-C33 info:eu-repo/grantAgreement/ES/MICINN/RYC2021-031526-I info:eu-repo/semantics/openAccess by https://creativecommons.org/licenses/by/4.0/deed.es info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Elduque, Eva 2006 440 Universidad de Zaragoza Dpto. Matemáticas Área Geometría y Topología 120, 3 (2026), [19 pp.] Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas 1578-7303 463423 http://zaguan.unizar.es/record/170400/files/texto_completo.pdf Versión publicada 1349813 http://zaguan.unizar.es/record/170400/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:170400 articulos driver 2026-04-18-10:48:51 ARTICLE