On some K3 surfaces with order sixteen automorphism

Paola Comparin; Nathan Priddis; Alessandra Sarti

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arXiv · 1912.09803

On some K3 surfaces with order sixteen automorphism

Paola Comparin·Nathan Priddis·Alessandra Sarti

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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.

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Paola Comparin, Nathan Priddis, Alessandra Sarti. 2019-12-20. On some K3 surfaces with order sixteen automorphism. https://arxiv.org/abs/1912.09803

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