Galois skew lines of smooth surfaces in P3

It is known that the degree of irrationality irr(X) of a smooth surface X of degree d >= 5 in P-3 is at least d - 2. In this paper, we study a Galois rational map f : X -> P-2 of degree d - 2, and we show that the Galois group of f is a cyclic group, and f is defined by the family of lines intersecting two fixed skew lines. In addition, we give a necessary and sufficient condition that X has skew lines which give a Galois rational map of degree d - 2 by using automorphisms of X.