Mirror symmetry and partial compactifications of k3 moduli | BIMSA AG Seminar

Abstract

I will talk about work with Hacking, Keel and Siebert on using miror constructions to providepartial compactifications of the moduli of K3 surfaces. Starting with a one-parameter maximallyunipotent degeneration of Picard rank 19 K3 surfaces, we construct, using methods of myself and Siebert, a mirror family which is defined in a formal neiahbourhood of a union of strata of a toricvariety whose fan is defined, to first approximation, as the Mori fan of the original degenerationThis formal family may then be glued in to the moduli space of polarized k3 surfaces to obtain apartial compactification. Perhaps the most significant by-product of this construction is theexistence of theta functions in this formal neiahbourhood, certain canonical bases for sections ofpowers of the polarizing line bundle.