Degeneration of K3 surfaces with non-symplectic automorphisms

Abstract

We prove that a K3 surface with an automorphism acting on the global 2-forms by a primitive m-th root of unity, m ≠ 1, 2, 3, 4, 6, does not degenerate (assuming the existence of the so-called Kulikov models). A key result used to prove this is the rationality of the actions of automorphisms on the graded quotients of the weight filtration of the l-adic cohomology groups of the surface.