  We 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.
