Abstract
It is known that the degree of irrationality of a smooth surface X of degree in is at least d – 2. In this paper, we study a Galois rational map 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.
2020 MATHEMATICS SUBJECT CLASSIFICATION: