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arXiv · 1612.07569

Degeneration of K3 surfaces with non-symplectic automorphisms

Yuya Matsumoto
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Abstract

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

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Yuya Matsumoto. 2016-12-22. Degeneration of K3 surfaces with non-symplectic automorphisms. https://doi.org/10.4171/rsmup%2F123

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