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Classification of order sixteen non-symplectic automorphisms on K3 surfaces

Alessandra Sarti|Dima Al Tabbaa|Shingo Taki
대한수학회 (The Korean Mathematical Society)|2016.11|대한수학회지 (Journal of the KMS)|제53권 제6호|pp. 1237-1260

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참고문헌

키워드

K3 surfacesnon-symplectic automorphisms
주제분류수학

초록

In the paper we classify complex K3 surfaces with non-sym\-plectic 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.

Abstract

In the paper we classify complex K3 surfaces with non-sym\-plectic 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.

참고문헌 (23)

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