Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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CLASSIFICATION OF ORDER SIXTEEN NON-SYMPLECTIC AUTOMORPHISMS ON K3 SURFACES

  • Tabbaa, Dima Al (Laboratoire de Mathematiques et Applications UMR CNRS 7348, Universite de Poitiers) ;
  • Sarti, Alessandra (Laboratoire de Mathematiques et Applications UMR CNRS 7348, Universite de Poitiers) ;
  • Taki, Shingo (Department of Mathematics Tokai University)
  • Received : 2015.06.08
  • Published : 2016.11.01
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Abstract

In the paper we classify complex K3 surfaces with non-symplectic automorphism of order 16 in full generality. We show that the fixed locus contains only rational curves and points and we completely classify the seven possible configurations. If the Picard group has rank 6, there are two possibilities and if its rank is 14, there are five possibilities. In particular if the action of the automorphism is trivial on the Picard group, then we show that its rank is six.

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References

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