Algebraic Geometry Seminar

In the mid-1990s, physicists Berglund and Hubsch proposed a way to construct a mirror partner for a certain kind of Calabi-Yau variety. When the variety has dimension 2, these are examples of K3 surfaces. Around the same time, Dolgachev and others conceived of a version of mirror symmetry that applies to more general families of K3 surfaces. We will introduce these special K3 surfaces, which are certain hypersurfaces in weighted projective space, and the question of compatibility between these two versions of mirror symmetry. While the question is open in general, we will highlight a collection of surfaces where it can be verified. This is joint work with Paola Comparin, Nathan Priddis, and Rachel Webb.