Mirror symmetry for lattice polarized K3 surfaces

Abstract

We establish a relationship between mirror symmetry for K3 surfaces and Arnold's strange duality for K3 surfaces. We compute various examples of mirror families. Among them the mirror moduli family for the moduli space of degree 2n polarized K3 surfaces. It turns out to be related to the moduli space of elliptic curves with level n.

40 pages, Plain TEX; Expanded and revised version. Some new results are added; For example, we describe a relationship between mirror families of degree 2n polarized K3 surfaces and families of elliptic curves of level n

References in corpus (3)

• Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties
• String Theory on K3 Surfaces
• Duality of Weights, Mirror Symmetry and Arnold's Strange Duality

Cited by in corpus (7)

• Toric Degenerations of Fano Threefolds Giving Weak Landau-Ginzburg Models
• Mirror Symmetry for $G_2$-Manifolds: Twisted Connected Sums and Dual Tops
• Strange duality, mirror symmetry, and the Leech lattice
• K3 Surfaces with Involution and Analytic Torsion
• Parabolic Higgs bundles, $t{t}^{\ast }$ connections and opers
• Fano-Mathieu correspondence
• Examples of lattice-polarized K3 surfaces with automorphic discriminant, and Lorentzian Kac--Moody algebras