Work

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

Year: 2025

Type: article

Abstract: 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 C_{p,q} curves and torus-type projective sextics, and describing the conditions under which this phenomenon occurs.

Source: Revista Matemática Iberoamericana

DOI: 10.4171/rmi/1550

Authors: José I. Cogolludo-Agustín, Eva Elduque

Institutions: Universidad de Zaragoza, Universidad Autónoma de Madrid

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: European Commission, Gobierno de Aragón, Agencia Estatal de Investigación