Greatest lower bounds on Ricci curvature for toric Fano manifolds

DOI10.1016/j.aim.2010.12.023zbMath1222.14090arXiv0909.3443OpenAlexW1999424365MaRDI QIDQ633601

Chi Li

Publication date: 29 March 2011

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0909.3443

zbMATH Keywords

Ricci curvaturetoric Fano manifold

Mathematics Subject Classification ID

Fano varieties (14J45) Local differential geometry of Hermitian and Kählerian structures (53B35)

Related Items (22)

On K-stability and the volume functions of ℚ-Fano varieties: Table 1. ⋮ K-stability of Gorenstein Fano group compactifications with rank two ⋮ Kähler-Einstein metrics along the smooth continuity method ⋮ Basis log canonical thresholds, local intersection estimates, and asymptotically log del Pezzo surfaces ⋮ Connecting toric manifolds by conical Kähler-Einstein metrics ⋮ Real Monge-Ampère equations and Kähler-Ricci solitons on toric log Fano varieties ⋮ Conical Kähler-Einstein metrics revisited ⋮ Greatest Ricci lower bounds of projective horospherical manifolds of Picard number one ⋮ The Kähler-Ricci flow and quantitative bounds for Donaldson-Futaki invariants of optimal degenerations ⋮ Basis divisors and balanced metrics ⋮ On the constant scalar curvature Kähler metrics (II)—Existence results ⋮ Coupled complex Monge-Ampère equations on Fano horosymmetric manifolds ⋮ K-stability of Fano varieties: an algebro-geometric approach ⋮ Kähler-Einstein metrics: old and new ⋮ On the limit behavior of metrics in the continuity method for the Kähler–Einstein problem on a toric Fano manifold ⋮ Kähler-Einstein metrics on group compactifications ⋮ A variational approach to the Yau–Tian–Donaldson conjecture ⋮ Thresholds, valuations, and K-stability ⋮ Delta invariants of projective bundles and projective cones of Fano type ⋮ Remarks on logarithmic K-stability ⋮ Greatest lower bounds on Ricci curvature of homogeneous toric bundles ⋮ Toric Kähler-Einstein metrics and convex compact polytopes

Cites Work

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• On Kähler-Einstein metrics on certain Kähler manifolds with \(C_ 1(M)>0\)
• An obstruction to the existence of Einstein Kaehler metrics
• Kähler--Ricci solitons on toric manifolds with positive first Chern class
• Greatest lower bounds on the Ricci curvature of Fano manifolds
• Kahler geometry on toric manifolds, and some other manifolds with large symmetry
• ON STABILITY OF THE TANGENT BUNDLES OF FANO VARIETIES
• On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I

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