Mirror constructions for K3 surfaces from bimodal singularities

2022/06/29 by Mase, Makiko, Whitcher, Ursula
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2206.14367

Abstract

We study lattice polarizations of five exceptional pairs of families of K3 surfaces obtained via compactifications of strange dual pairs of bimodal singularities. We show that the polarizations induced by embedding these paired families in paired toric varieties obtained from polar dual reflexive polytopes cannot be mirror lattices and identify mirror sublattices.

Related

• Mirror symmetry for lattice polarized K3 surfaces
• Reflexive Polytopes and Lattice-Polarized K3 Surfaces
• Lattice polarized toric K3 surfaces
• A note on bimodal singularities and mirror symmetry
• Polytope duality for families of K3 surfaces associated to singularities Q₁₆ and S₁₆