Back to Algebraic Geometry Seminar: Fall 2012
Algebraic Geometry Seminar
Date: Tuesday, Aug 28, 2012
Time: 3:30PM - 4:30PM
Location: JTB 120
Yi Zhu
University of Utah
Title |
Finding very free rational curves |
Abstract |
A rational curve on a smooth algebraic variety is very free if the pullback of the tangent bundle is positive. This notion is the key to the theory of rational curves and has various applications both in geometry and in arithmetics. In characteristic zero, the general theory of Kollar-Miyaoka-Mori predicts the existence of such curves on Fano varieties (or more generally, on rationally connected varieties). However, constructing very free curves is usually difficult, especially in arbitrary characteristic. In this talk, first I will survey basic results which motivate the search of very free curves. Then I will focus on several examples where we can construct them concretely. |
Algebraic Geometry