An effective weighted K-stability condition for polytopes and semisimple principal toric fibratons

Abstract

The second author has shown that existence of extremal Kähler metrics on semisimple principal toric fibrations is equivalent to a notion of weighted uniform K-stability, read off from the moment polytope. The purpose of this article is to prove various sufficient conditions of weighted uniform K-stability which can be checked effectively and explore the low dimensional new examples of extremal Kähler metrics it provides.

arXiv commentv3 following suggestions by the referee. To correct a mistake in the previous version, we restricted our setting to the case v >0 everywhere. This is enough for our applications. Final version, to appear in Annales Henry Lebesgue

References in corpus (8)

• Hamiltonian 2-forms in Kahler geometry, III Extremal metrics and stability
• Kahler geometry on toric manifolds, and some other manifolds with large symmetry
• Geodesic rays and stability in the cscK problem
• Stability and coercivity for toric polarizations
• Kähler metrics with constant weighted scalar curvature and weighted K-stability
• Real Monge-Ampere equations and Kahler-Ricci solitons on toric log Fano varieties
• Connecting toric manifolds by conical Kahler-Einstein metrics
• Uniform K-stability of polarized spherical varieties