Sai-Kee Yeung, Purdue U., USA

Geometry of a special arithmetic complex two ball quotient

Abstract

The purpose of the talk is to explain a joint work with Vincent Koziarz and Donald Cartwright on the geometry of a complex two ball quotient constructed earlier by Cartwright and Steger. The surface has the smallest possible Euler number 3 among surfaces of general type but is a not a fake projective plane. Basic geometric properties of the surface had not been understood, such as the genus of the Albanese fibration. We would answer some questions in this direction and use the example to study several problems in the geometry of algebraic surfaces and complex ball quotients.