Families of Homogeneous Spaces over Surfaces
Yi Zhu, Stony Brook

de Jong and Starr formulated the following principle: families of rationally simply connected (RSC) varieties over algebraic surfaces admit rational sections if certain Brauer-type obstructions vanish. The known RSC varieties are all of Picard number one, e.g., lower degree hypersurfaces and Grassmannians. In this talk, I will discuss how to define rational simple connectedness for varieties of higher Picard numbers. As an application, I will explain the proof of de Jong-Starr's principle for families of projective homogeneous spaces over surfaces.