Automorphisms of finite order on Gorenstein del Pezzo surfaces

In this paper we shall determine all actions of groups of prime order with on Gorenstein del Pezzo (singular) surfaces of Picard number 1. We show that every order- element in ( , being the minimal resolution of ) is lifted from a projective transformation of . We also determine when is finite in terms of , and the number of singular members in . In particular, we show that either for some , or for every prime , there is at least one element of order in (hence is infinite).