K3 surfaces from configurations of six lines in ${\mathbb{P}}^2$ and mirror symmetry I

Abstract

From the viewpoint of mirror symmetry, we revisit the hypergeometric system $E(3,6)$ for a family of K3 surfaces. We construct a good resolution of the Baily-Borel-Satake compactification of its parameter space, which admits special boundary points (LCSLs) given by normal crossing divisors. We find local isomorphisms between the $E(3,6)$ systems and the associated GKZ systems defined locally on the parameter space and cover the entire parameter space. Parallel structures are conjectured in general for hypergeometric system $E(n,m)$ on Grassmannians. Local solutions and mirror symmetry will be described in a companion paper \cite{HLTYpartII}, where we introduce a K3 analogue of the elliptic lambda function in terms of genus two theta functions.

34 pages, 5 figures; minor changes in the notation

References in corpus (1)

• GKZ-Generalized Hypergeometric Systems in Mirror Symmetry of Calabi-Yau Hypersurfaces

Cited by in corpus (1)

• K3 surfaces from configurations of six lines in ${\mathbb{P}}^2$ and mirror symmetry II --- ${\lambda }_{K3}$-functions ---