On the fundamental groups associated to contractions of extremal rays (Q2769832)

Let \(X\) be a normal proper variety, and \(f:X\to S\) be a surjective projective morphism of normal algebraic varieties with connected fibers. Suppose that there exists an effective \(\mathbb{Q}\)-divisor \(\Delta\) such that the log pair \((X, \Delta)\) is Kawamata log terminal and \(-(K_{X}+\Delta)\) is \(f\)-ample. The main result of the paper under review is the following: the induced homomorphism of the fundamental groups \(f_{*}:\pi_{1}(X)\to\pi_{1}(S)\) is an isomorphism. The author also considers a generalization of the latter result.