Degeneration of K3 surfaces with non-symplectic automorphisms

  • Yuya Matsumoto

    Tokyo University of Science, Chiba-ken, Japan
Degeneration of K3 surfaces with non-symplectic automorphisms cover
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Abstract

We prove that a K3 surface with an automorphism acting on the global 22-forms by a primitive mm-th root of unity, m1,2,3,4,6m \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 ll-adic cohomology groups of the surface.

Cite this article

Yuya Matsumoto, Degeneration of K3 surfaces with non-symplectic automorphisms. Rend. Sem. Mat. Univ. Padova (2023),

DOI 10.4171/RSMUP/123