Back to Algebraic Geometry Seminar: Spring 2012
Algebraic Geometry Seminar
Date: Tuesday, Jan 24, 2012
Time: 3:30PM - 4:30PM
Location: LCB 222
Yi Zhu
Stony Brook
Title |
Families of Homogeneous Spaces over Curves |
Abstract |
A basic question in arithmetic geometry is whether a given variety defined over a non-closed field admits a rational point. When the base field is of geometric nature, i.e., function fields of varieties, one naturally hopes to solve the problem via purely geometric methods. In this talk, I will discuss the geometry of the moduli space of sections of a projective homogeneous space fibration over an algebraic curve and its MRC quotient. By the results of Esnault and Graber-Harris-Starr, it leads to answers for the existence of rational points on projective homogeneous spaces defined either over a global function field or over a function field of an algebraic surface. |
Algebraic Geometry