Quotients of del Pezzo surfaces of high degree

Abstract

In this paper we study quotients of del Pezzo surfaces of degree four and more over arbitrary field k \Bbbk of characteristic zero by finite groups of automorphisms. We show that if a del Pezzo surface X X contains a point defined over the ground field and the degree of X X is at least five, then the quotient is always k \Bbbk -rational. If the degree of X X is equal to four, then the quotient can be non- k \Bbbk -rational only if the order of the group is 1 1 , 2 2 , or 4 4 . For these groups we construct examples of non- k \Bbbk -rational quotients.