Kummer surfaces associated with Seiberg–Witten curves

By carrying out a rational transformation on the base curve CP1CP1 of the Seiberg–Witten curve for N=2N=2 supersymmetric pure SU(2)-gauge theory, we obtain a family of Jacobian elliptic K3 surfaces of Picard rank 1717. The isogeny relating the Seiberg–Witten curve for pure SU(2)-gauge theory to the one for SU(2)-gauge theory with Nf=2Nf=2 massless hypermultiplets extends to define a Nikulin involution on each K3 surface in the family. We show that the desingularization of the quotient of the K3 surface by the involution is isomorphic to a Kummer surface of the Jacobian variety of a curve of genus two. We then derive a relation between the Yukawa coupling associated with the elliptic K3 surface and the Yukawa coupling of pure SU(2)-gauge theory.