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000170400 005__ 20260420103354.0
000170400 0247_ $$2doi$$a10.1007/s13398-026-01853-1
000170400 0248_ $$2sideral$$a148905
000170400 037__ $$aART-2026-148905
000170400 041__ $$aeng
000170400 100__ $$0(orcid)0000-0003-1820-6755$$aCogolludo-Agustín, José I.$$uUniversidad de Zaragoza
000170400 245__ $$aOn the topology of fiber-type curves: an affine Zariski pair of nodal curves
000170400 260__ $$c2026
000170400 5060_ $$aAccess copy available to the general public$$fUnrestricted
000170400 5203_ $$aIn 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.
000170400 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E22-20R$$9info:eu-repo/grantAgreement/ES/MCIU/PID2024-156181NB-C33$$9info:eu-repo/grantAgreement/ES/MICINN/RYC2021-031526-I
000170400 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttps://creativecommons.org/licenses/by/4.0/deed.es
000170400 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000170400 700__ $$aElduque, Eva
000170400 7102_ $$12006$$2440$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Geometría y Topología
000170400 773__ $$g120, 3 (2026), [19 pp.]$$pRev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat.$$tRevista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas$$x1578-7303
000170400 8564_ $$s463423$$uhttps://zaguan.unizar.es/record/170400/files/texto_completo.pdf$$yVersión publicada
000170400 8564_ $$s1349813$$uhttps://zaguan.unizar.es/record/170400/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada
000170400 909CO $$ooai:zaguan.unizar.es:170400$$particulos$$pdriver
000170400 951__ $$a2026-04-18-10:48:51
000170400 980__ $$aARTICLE