000118617 001__ 118617 000118617 005__ 20230519145520.0 000118617 0247_ $$2doi$$a10.1017/S0013091521000675 000118617 0248_ $$2sideral$$a126808 000118617 037__ $$aART-2021-126808 000118617 041__ $$aeng 000118617 100__ $$0(orcid)0000-0003-1820-6755$$aCogolludo J.I.$$uUniversidad de Zaragoza 000118617 245__ $$aFree quotients of fundamental groups of smooth quasi-projective varieties 000118617 260__ $$c2021 000118617 5060_ $$aAccess copy available to the general public$$fUnrestricted 000118617 5203_ $$aWe study the fundamental groups of the complements to curves on simply connected surfaces, admitting non-abelian free groups as their quotients. We show that given a subset of the Néron-Severi group of such a surface, there are only finitely many classes of equisingular isotopy of curves with irreducible components belonging to this subset for which the fundamental groups of the complement admit surjections onto a free group of a given sufficiently large rank. Examples of subsets of the Néron-Severi group are given with infinitely many isotopy classes of curves with irreducible components from such a subset and fundamental groups of the complements admitting surjections on a free group only of a small rank. © The Author(s) 2021. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society. 000118617 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/ 000118617 590__ $$a1.088$$b2021 000118617 591__ $$aMATHEMATICS$$b134 / 333 = 0.402$$c2021$$dQ2$$eT2 000118617 592__ $$a0.796$$b2021 000118617 593__ $$aMathematics (miscellaneous)$$c2021$$dQ1 000118617 594__ $$a1.4$$b2021 000118617 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/submittedVersion 000118617 700__ $$aLibgober A. 000118617 7102_ $$12006$$2440$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Geometría y Topología 000118617 773__ $$g64, 4 (2021), 924-946$$pProc. Edinb. Math. Soc.$$tPROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY$$x0013-0915 000118617 8564_ $$s519515$$uhttps://zaguan.unizar.es/record/118617/files/texto_completo.pdf$$yPreprint 000118617 8564_ $$s1865097$$uhttps://zaguan.unizar.es/record/118617/files/texto_completo.jpg?subformat=icon$$xicon$$yPreprint 000118617 909CO $$ooai:zaguan.unizar.es:118617$$particulos$$pdriver 000118617 951__ $$a2023-05-18-15:22:30 000118617 980__ $$aARTICLE