Corpus ID: 119154853

Degeneration of K3 surfaces with non-symplectic automorphisms

@article{Matsumoto2016DegenerationOK,
  title={Degeneration of K3 surfaces with non-symplectic automorphisms},
  author={Y. Matsumoto},
  journal={arXiv: Algebraic Geometry},
  year={2016}
}
  • Y. Matsumoto
  • Published 2016
  • Mathematics
  • arXiv: Algebraic Geometry
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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References

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