2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/149980We discuss the applications of fundamental groups (of complements of curves) computations (and possibly the computations of the second homotopy group as a model over it) to the classification of algebraic surface. We prove that the fundamental group of the complement of the branch curve of a generic projection of a Veronese surface to the complex plane is an "almost solvable" group in the sense that it contains a solvable group of finite index and thus we can consider the second fundamental group as model over the first.To be published in IMCP 9 (Proceedings of Hirzebruch 65-birthday)Algebraic Geometrytext