The fundamental group of the complement of the branch curve of the second Hirzebruch surface

In this paper we prove that the Hirzebruch surface F2,(2,2)F2,(2,2) embedded in CP17CP17 supports the conjecture on the structure and properties of fundamental groups of complement of branch curves of generic projections, as laid out in [M. Teicher, New Invariants for surfaces, Contemp. Math. 231 (1999) 271–281]. We use the regeneration from [M. Friedman, M. Teicher, The regeneration of a 5-point, Pure and Applied Mathematics Quarterly 4 (2) (2008) 383–425. Fedor Bogomolov special issue, part I], the van Kampen theorem and properties of B̃n-groups [M. Teicher, On the quotient of the braid group by commutators of transversal half-twists and its group actions, Topology Appl. 78 (1997) 153–186], where B̃n is a quotient of the braid group BnBn, for n=16n=16.