Correspondence Between Elliptic-Elliptic Surfaces and K3 Surfaces

Explore a mathematical lecture where Yilong Zhang from Purdue University discusses the correspondence between elliptic-elliptic surfaces and K3 surfaces. Learn about elliptic-elliptic surfaces, which are elliptic surfaces over genus one curves with p_g=1, and how their H^2 carries a K3-type Hodge structure isometric to a Hodge substructure of a K3 surface with an E8 polarization. The lecture examines how the Hodge conjecture predicts an algebraic correspondence between their transcendental Hodge structures, suggesting a geometric relationship between these surfaces. Discover the findings from Zhang's joint work with Arapura and Greer, demonstrating this correspondence for specific examples arising from rational double cover of Kummer surfaces, which generalizes Shioda-Inose's work from the 1970s.