Modular invariants for lattice polarized K3 surfaces

Abstract

We study the class of complex algebraic K3 surfaces admitting an embedding of HE8 � E8 inside the Neron-Severi lattice. These special K3 surfaces are classified by a pair of modular invariants, in the same manner that ellipticcurves over C are classifiedby the J-invariant. Via the canonical Shioda-Inose structure we construct a geometric correspondence relating K3 surfaces of the above type with abelian surfaces realized as cartesian products of two elliptic curves. We then use this correspondence to determine explicit formulas for the modular invariants.