Scalar Curvature and Stability of Toric Fibrations

2012/12/28 by Thomas William Nyberg, Nyberg, Thomas
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1212.6572

openalex publication_date 2012/12/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study fibrations \cV of toric varieties over the flag variety G/T, where G is a compact semisimple Lie group and T is a maximal torus. From symplectic data, we construct test configurations of \cV and compute their Futaki invariants by employing a generalization of Pick's Theorem. We also give a simple form of the Mabuchi Functional.

Citations

• Interior estimates for solutions of Abreu's equation
• Kahler geometry on toric manifolds, and some other manifolds with large symmetry
• Lectures on Stability and Constant Scalar Curvature

Related

• Families of toric varieties
• Stability Functions
• Matroids and Geometric Invariant Theory of torus actions on flag spaces
• Toroidal and toric models of fibrations over curves
• Fibrations, and stability for compact group actions on manifolds with local bounded Ricci covering geometry