On Dolgachev–Nikulin Duality for Fibers of Landau–Ginzburg Models of Smooth Fano Threefolds

Mirror Symmetry corresponds to Fano varieties certain one-dimensional families which are called Landau–Ginzburg models. Elements of these families are expected to be Calabi–Yau varieties mirror dual to anticanonical sections of Fano varieties. In the three-dimensional case one of the forms of Mirror Symmetry conjecture is provided by Dolgachev–Nikulin duality of K3 surfaces. This conjecture was proved by Ilten–Lewis–Przyjalkowski in the case of Picard rank 1. In the talk we will discuss the obtained results for Picard rank 2.