Conical Calabi-Yau metrics on toric affine varieties and convex cones

DOI10.4310/jdg/1696432924arXiv2005.07053MaRDI QIDQ6183880

Robert J. Berman

Publication date: 4 January 2024

Published in: Journal of Differential Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2005.07053

zbMATH Keywords

toric varietyCalabi-Yau varietySasaki-Einstein metrics

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Cites Work

• Real Monge-Ampère equations and Kähler-Ricci solitons on toric log Fano varieties
• Gromov-Hausdorff limits of Kähler manifolds and algebraic geometry
• Potential functions and actions of tori on Kähler manifolds
• Einstein metrics on spheres
• Toric geometry, Sasaki-Einstein manifolds and a new infinite class of AdS/CFT duals
• The geometric dual of \(a\)-maximisation for toric Sasaki-Einstein manifolds
• Sasaki-Einstein manifolds and volume minimisation
• Uniqueness and examples of compact toric Sasaki-Einstein metrics
• Obstructions to the existence of Sasaki-Einstein metrics
• Superconformal field theory on threebranes at a Calabi-Yau singularity
• Minimizing normalized volumes of valuations
• Estimation of Sobolev embedding constant on a domain dividable into bounded convex domains
• Gromov-Hausdorff limits of Kähler manifolds and algebraic geometry. II
• K-semistability for irregular Sasakian manifolds
• Non-spherical horizons. I
• Kähler--Ricci solitons on toric manifolds with positive first Chern class
• Sasaki-Einstein metrics and K-stability
• The uniform version of Yau-Tian-Donaldson conjecture for singular Fano varieties
• Convergence rates for discretized Monge-Ampère equations and quantitative stability of optimal transport
• Transverse Kähler geometry of Sasaki manifolds and toric Sasaki-Einstein manifolds
• Sasaki-Einstein metrics on \(S^2\times S^3\)
• From Monge-Ampère equations to envelopes and geodesic rays in the zero temperature limit
• Frankel conjecture and Sasaki geometry
• KÄHLER–EINSTEIN METRICS WITH CONE SINGULARITIES ON KLT PAIRS
• On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I
• Singularities of Pairs
• Kähler–Einstein metrics, canonical random point processes and birational geometry
• Stability of algebraic varieties and Kähler geometry
• Algebraicity of the metric tangent cones and equivariant K-stability
• Toric pluripotential theory
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item