On K3 surfaces of Picard rank 14

Abstract

We study complex algebraic K3 surfaces with finite automorphism groups and polarized by rank-fourteen, 2-elementary lattices. Three such lattices exist, namely $H\oplus E_8(-1)\oplus A_1(-1{)}^{\oplus 4}$, $H\oplus E_8(-1)\oplus D_4(-1)$, and $H\oplus D_8(-1)\oplus D_4(-1)$. As part of our study, we provide birational models for these surfaces as quartic projective hypersurfaces and describe the associated coarse moduli spaces in terms of suitable modular invariants. Additionally, we explore the connection between these families and dual K3 families related via the Nikulin construction.

51 pages

References in corpus (6)

• K3 surfaces, modular forms, and non-geometric heterotic compactifications
• Discrete gauge groups in certain F-theory models in six dimensions
• Non-Geometric F-Theory-Heterotic Duality
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Cited by in corpus (1)

• On two-elementary K3 surfaces with finite automorphism group