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## Banach Center Publications

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## Order eight non-symplectic automorphisms on elliptic K3 surfaces

### Volume 116 / 2018

Banach Center Publications 116 (2018), 11-24 MSC: Primary: 14J28; Secondary: 14J50, 14J10. DOI: 10.4064/bc116-1

#### Abstract

In this paper we classify complex $K3$ surfaces with non-symplectic automorphism of order 8 that leaves invariant a smooth elliptic curve. We show that the rank of the Picard group is either $10$, $14$ or $18$ and the fixed locus is the disjoint union of elliptic curves, rational curves and points, whose number does not exceed $1$, $2$, respectively $14$. We give examples corresponding to several types of fixed locus in the classification.

#### Authors

• Dima Al TabbaaLaboratoire de Mathématiques et Applications
UMR CNRS 7348
Université de Poitiers
Téléport 2
Boulevard Marie et Pierre Curie
86962 Futuroscope Chasseneuil, France
e-mail
• Alessandra SartiLaboratoire de Mathématiques et Applications
UMR CNRS 7348
Université de Poitiers
Téléport 2
Boulevard Marie et Pierre Curie
86962 Futuroscope Chasseneuil, France
e-mail

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