The mirror symmetry of K3 surfaces with non-symplectic automorphisms of   prime order
  We consider K3 surfaces that possess certain automorphisms of prime order p>2 and we present, for these surfaces, a correspondence between the mirror symmetry of Berglund-Huebsch-Chiodo-Ruan and that for lattice polarized K3 surfaces presented by Dolgachev. 
Paola Comparin, Christopher Lyons, Nathan Priddis, Rachel Suggs
math.AG hep-th math-ph math.MP