Non-symplectic automorphisms of order 3, 4, and 6 of K3 surfaces with smooth quotient.

Let X be a K3 surface, and g be a primitive non-symplectic automorphism of X of order 3, 4, or 6. We write the quotient space as X / 〈 g 〉 and the quotient morphism as p : X → X / 〈 g 〉 . In this paper, we study curves on X obtained by pulling back curves on X / 〈 g 〉 by p. As a result, we show that if X / 〈 g 〉 is smooth, then X / 〈 g 〉 is the projective plane ℙ 2 or Hirzebruch surfaces F l of degree l = 0 , 1 , 2 , 3 , 4 , 6 , or 12. In addition, we show that if X / 〈 g 〉 is smooth, then X / 〈 g 〉 is determined by the set of fixed points of g and the action of g on rational curves on X. [ABSTRACT FROM AUTHOR]