2018/10/01 by Hosono, Shinobu, Lian, Bong H., Takagi, Hiromichi +1
#Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1810.00606
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 \citeHLTYpartII, where we introduce a K3 analogue of the elliptic lambda function in terms of genus two theta functions.