Kummer surfaces associated with Seiberg-Witten curves
The author gives an explicit construction of a family of Jacobian elliptic \(K3\) surfaces with high Picard rank. More explicitly, by applying a rational transformation to the base curve \(\mathbb{CP}^{1}\) of the Seiberg-Witten curve for \(\mathcal{N}=2\) supersymmetric pure \(SU(2)\)-gauge theory, the author obtains a family of Jacobian elliptic \(K3\) surfaces of Picard rank 17. In this work, it is also shown that the desingularization of the quotient of \(K3\) surface by an involution is isomorphic to a Kummer surface of the Jacobian variety of a curve of genus two.
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