2013/12/25 by Trepalin, Andrey
#Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1312.6904
In this paper we study quotients of del Pezzo surfaces of degree four and more over arbitrary field \Bbbk of characteristic zero by finite groups of automorphisms. We show that if a del Pezzo surface X contains a point defined over the ground field and the degree of X is at least five then the quotient is always \Bbbk-rational. If the degree of X is equal to four then the quotient can be non-\Bbbk-rational only if the order of the group is 1, 2 or 4. For these groups we construct examples of non-\Bbbk-rational quotients.