Constant Scalar Curvature of Toric Fibrations
We study the conditions under which a fibration of toric varieties, fibered over a flag variety, admits a constant scalar curvature Kähler metric. We first provide an introduction to toric varieties and toric fibrations and derive the scalar curvature equation. Next we derive interior a priori estimates of all orders and a global L^∞-estimate for the scalar curvature equation. Finally we extend the theory of K-Stability to this setting and construct test-configurations for these spaces.
Academic Commons
Nyberg, Thomas
Author
Phong, Duong Hong
Thesis advisor
Columbia University. Mathematics
Originator
Theses
English
Mathematics
text
2014
eng
2017-06-08T20:18:27Z
2017-11-10T04:14:12Z
Ph.D.
2
Mathematics
Columbia University
10.7916/D8TH8JVH