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.
