Remarks on fundamental groups of complements of divisors on algebraic varieties (Q1340425)

Let \(V\) be a smooth projective variety, \(D \subset V\) a divisor and \(L\) the corresponding line bundle on \(V\). Let \(s : V \backslash D \to L^\times\) be a section, where \(L^\times = L \backslash \{\) the zero section\}. In this paper new conditions are given under which \(s\) induces an isomorphism of fundamental groups. As an application, some fundamental groups of singular curve complements are computed.