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

arXiv commentSection 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 (30)

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• The Cauchy problem for the homogeneous Monge-Ampere equation, II. Legendre transform
• The Kähler geometry of Bott manifolds
• Kahler-Einstein metrics on symmetric Fano T-varieties
• Quasi-projectivity of the moduli space of smooth Kahler-Einstein Fano manifolds
• 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
• On the classification of Kahler-Ricci solitons on Gorenstein del Pezzo surfaces
• Compact moduli space of Kahler-Einstein Fano varieties
• Deformations of complex structures and the coupled Kähler-Yang-Mills equations
• Kähler-Ricci solitons on horospherical variety
• Ricci flat Kähler metrics on rank two complex symmetric spaces
• Kaehler-Einstein Fano threefolds of degree 22
• Modified Futaki invariant and equivariant Riemann-Roch formula
• Multiplier ideal sheaves and the Kähler-Ricci flow on toric Fano manifolds with large symmetry
• The Kahler-Ricci flow and K-stability
• Ancient Ricci Flow Solutions on Bundles
• An effective weighted K-stability condition for polytopes and semisimple principal toric fibratons
• Kähler-Einstein metrics and higher alpha-invariants
• Greatest lower bounds on Ricci curvature for toric Fano manifolds
• Some Estimates for a Generalized Abreu's Equation
• Scalar Curvature and Stability of Toric Fibrations
• Multiplier ideal sheaves and geometric problems
• On the Kähler-Ricci flows near the Mukai-Umemura 3-fold
• Toric extremal Kaehler-Ricci solitons are Kaehler-Einstein