EVENT DETAILS AND ABSTRACT

Title: An elliptic surface with maximal Picard number
Speaker: Yilong Zhang
Speaker Info: Purdue University
Brief Description:
Special Note:
Abstract:

For a smooth algebraic surface over complex numbers, the Picard number $\rho$ is bounded above by the Hodge number $h^{1,1}$. A surface has maximal Picard number if $\rho=h^{1,1}$. Examples of this kind are rare, particularly when the Kodaira dimension is at least zero. Shioda's modular surface S(N) is the universal family of elliptic curves with the level N structure. It is an elliptic surface with a maximal Picard number. When N is large, it has Kodaira dimensions one. However, such a surface has only torsion sections. The natural question is, is there an example of Kodaira dimension one elliptic surface with maximal Picard number and has nonzero Mordell-Weil rank? In joint work with Donu Arapura, we answer the question positively. We found an elliptic surface over an elliptic curve with maximal Picard number, together with a section of infinite order.