On some K3 surfaces with order sixteen automorphism

TL;DR

This paper studies K3 surfaces with Picard rank 14 that have a specific order 16 automorphism, analyzing their invariant lattices and elliptic fibrations to understand their moduli and mirror symmetry properties.

Contribution

It provides explicit computations of invariant lattices for these K3 surfaces and demonstrates their elliptic fibrations using geometric methods.

Findings

Invariant sublattices computed for K3 surfaces with order 16 automorphisms.

All such K3 surfaces admit elliptic fibrations.

Lattice computations aid in studying moduli spaces and mirror symmetry.

Abstract

We consider K3 surfaces of Picard rank 14 which admit a purely nonsymplectic automorphism of order 16. The automorphism acts on the second cohomology group with integer coefficients and we compute the invariant sublattice for the action. We show that all of these K3 surfaces admit an elliptic fibration and we compute the invariant lattices in a geometric way by using special curves of the elliptic fibration. The computation of these lattices plays an important role when one wants to study moduli spaces and mirror symmetry for lattice polarized K3 surfaces.