Kahler geometry on toric manifolds, and some other manifolds with large symmetry

Abstract

This is an expository article. Among other topics, we discuss the existence of Kahler-Ricci soliton metrics on toric Fano manifolds, and Kahler-Einstein metrics on deformations of the Mukai-Umemura 3-fold

Section 3.3 has been changed to correct a mistake in the original version

References in corpus (1)

• Constant scalar curvature metrics on toric surfaces

Cited by in corpus (13)

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• Weighted K-stability and coercivity with applications to extremal Kahler and Sasaki metrics
• SYZ conjecture for Calabi-Yau hypersurfaces in the Fermat family
• Numerical approximations to extremal metrics on toric surfaces
• Compact moduli space of Kahler-Einstein Fano varieties
• Modified Futaki invariant and equivariant Riemann-Roch formula
• Multiplier ideal sheaves and the Kähler-Ricci flow on toric Fano manifolds with large symmetry
• An effective weighted K-stability condition for polytopes and semisimple principal toric fibratons
• Greatest lower bounds on Ricci curvature for toric Fano manifolds
• Kähler-Einstein metrics and higher alpha-invariants
• Toric extremal Kaehler-Ricci solitons are Kaehler-Einstein
• Scalar Curvature and Stability of Toric Fibrations
• Multiplier ideal sheaves and geometric problems