Quasi-projective varieties whose fundamental group is a free product of cyclic groups

Cogolludo-Agustín, José I. (Universidad de Zaragoza) ; Elduque, Eva

Resumen: 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.

Idioma: Inglés

DOI: 10.4171/RMI/1550

Año: 2025

Publicado en: REVISTA MATEMATICA IBEROAMERICANA 41, 5 (2025), 1759-1794
ISSN: 0213-2230

Financiación: info:eu-repo/grantAgreement/ES/DGA/E22-20R
Financiación: info:eu-repo/grantAgreement/ES/MICINN/PID2020-114750GB-C31/AEI/10.13039/501100011033
Financiación: info:eu-repo/grantAgreement/ES/MICINN/RYC2021-031526-I

Tipo y forma: Article (Published version)

Área (Departamento): Área Geometría y Topología (Dpto. Matemáticas)