Symmetries of order four on K3 surfaces

抄録

In this paper we study automorphisms of order four on K3 surfaces. We give a classification of the non-symplectic ones when either the square of the automorphism is symplectic, or its fixed locus contains a curve of positive genus, or its fixed locus contains at least a curve and all the curves fixed by its square are rational. We provide partial results in the other cases.