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Constant Scalar Curvature of Toric Fibrations

Nyberg, Thomas

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.

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More About This Work

Academic Units
Mathematics
Thesis Advisors
Phong, Duong Hong
Degree
Ph.D., Columbia University
Published Here
July 7, 2014
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