Mirror symmetry for K3 surfaces

Abstract

For certain K3 surfaces, there are two constructions of mirror symmetry that are very different. The first, known as BHK mirror symmetry, comes from the Landau-Ginzburg model for the K3 surface; the other, known as LPK3 mirror symmetry, is based on a lattice polarization of the K3 surface in the sense of Dolgachev's definition. There is a large class of K3 surfaces for which both versions of mirror symmetry apply. In this class we consider the K3 surfaces admitting a certain purely nonsymplectic automorphism of order 4, 8, or 12, and we complete the proof that these two formulations of mirror symmetry agree for this class of K3 surfaces.

arXiv comment26 pages

References in corpus (10)

• Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties
• A Generalized Construction of Mirror Manifolds
• FJRW rings and Landau-Ginzburg Mirror Symmetry
• Landau-Ginzburg/Calabi-Yau correspondence, global mirror symmetry and Orlov equivalence
• Elliptic Gromov - Witten invariants and the generalized mirror conjecture
• The Mirror Map for Invertible LG Models
• A Landau--Ginzburg mirror theorem without concavity
• Lines generate the Picard groups of certain Fermat surfaces
• Picard lattices of families of K3 surfaces
• Semi-Calabi-Yau orbifolds and mirror pairs