We prove that a K3 surface with an automorphism acting on the global $2$\-forms by a primitive $m$\-th root of unity, $m \neq 1,2,3,4,6$, 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.

具有非对称自同构的K3曲面的退化

松本由雅

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