This work is concerned with computing the invariant lattices of purely non-symplectic automorphisms of special elliptic K3 surfaces. Brandhorst gave a collection of K3 surfaces admitting purely non-symplectic automorphisms that are uniquely determined up to isomorphism by certain invariants. For many of these surfaces, the automorphism is also unique or the automorphism group of the surface is finite and with a nice isomorphism class. Understanding the invariant lattices of these automorphisms and surfaces is interesting because of these uniqueness properties and because it is possible to give explicit generators for the Picard and invariant lattices. We use the methods given by Comparin, Priddis and Sarti to describe the Picard lattice in terms of certain special curves from the elliptic fibration of the surface. We use symmetries of the Picard lattice and fixed-point theory to compute the invariant lattices explicitly. This is done for all of Brandhorst's elliptic K3 surfaces having trivial Mordell-Weil group.
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BYU ScholarsArchive Citation
Fullwood, Joshua Joseph, "Invariant Lattices of Several Elliptic K3 Surfaces" (2021). Theses and Dissertations. 9188.
elliptic surfaces, purely non-symplectic automorphisms, k3 surfaces