162831 20251017144653.0 doi 10.4171/RMI/1550 sideral 145378 ART-2025-145378 eng Cogolludo-Agustín, José I. Universidad de Zaragoza (orcid)0000-0003-1820-6755 Quasi-projective varieties whose fundamental group is a free product of cyclic groups 2025 Access copy available to the general public Unrestricted In the context of Serre’s question, we study smooth complex quasi-projective varieties whose fundamental group is a free product of cyclic groups. In particular, we focus on the case of surfaces and prove the existence of an admissible map from such a quasi-projective surface to a smooth complex quasi-projective curve. Associated with this result, we prove addition-deletion lemmas which describe a natural operation correlating this family of quasi-projective surfaces and groups. Our methods also allow us to produce examples of curves in smooth projective surfaces whose complements have free products of cyclic groups as fundamental groups, generalizing classical results on Cp,q​ curves and torus-type projective sextics, and describing the conditions under which this phenomenon occurs. info:eu-repo/grantAgreement/ES/DGA/E22-20R info:eu-repo/grantAgreement/ES/MICINN/PID2020-114750GB-C31/AEI/10.13039/501100011033 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 41, 5 (2025), 1759-1794 Rev. mat. iberoam. REVISTA MATEMATICA IBEROAMERICANA 0213-2230 679229 http://zaguan.unizar.es/record/162831/files/texto_completo.pdf Versión publicada 1486541 http://zaguan.unizar.es/record/162831/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:162831 articulos driver 2025-10-17-14:37:11 ARTICLE