We study the rigid limit of type IIB string theory, compactified on a K3 fi
bration, which, near its conifold limit, contains the Seiberg-Witten curve
for N = 2 SU(2) super-Yang-Mills with a massive hypermultiplet in the funda
mental representation. Instead of working with an ALE approximation, we tre
at the K3 fibration globally. The periods we obtain in this way, allow for
an embedding of the field theory into a supergravity model.