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.

Country

United States

Related Organizations

Columbia University
United States
Columbia University Libraries, Open Scholarship Services
United States
Columbia University Libraries, Digital Scholarship
United States

Keywords

Riemannian, Geometry, 500, Toric varieties, 510, Fiberings (Mathematics), FOS: Mathematics, Mathematics, Kählerian manifolds

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