K3 Surfaces Associated with Curves of Genus Two

It is known ([10, 27]) that there is a unique K3 surface X which corresponds to a genus 2 curve C such that X has a Shioda–Inose structure with quotient birational to the Kummer surface of the Jacobian of C. In this paper we give an explicit realization of X as an elliptic surface over ℙ¹ with specified singular fibers of type II* and III*. We describe how the Weierstrass coefficients are related to the Igusa–Clebsch invariants of C.