The volume of Kähler-Einstein Fano varieties and convex bodies

DOI10.1515/crelle-2014-0069zbMath1358.53075arXiv1204.1308OpenAlexW2962993657MaRDI QIDQ507463

Robert J. Berman, Bo Berndtsson

Publication date: 6 February 2017

Published in: Journal für die Reine und Angewandte Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1204.1308

zbMATH Keywords

convex geometryholomorphic \({\mathbb{C}^{*}}\)-actionrational polytopesStein domains

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Fano varieties (14J45) Kähler-Einstein manifolds (32Q20)

Related Items

Improved bounds for Hadwiger's covering problem via thin-shell estimates ⋮ On K-stability and the volume functions of ℚ-Fano varieties: Table 1. ⋮ Real Monge-Ampère equations and Kähler-Ricci solitons on toric log Fano varieties ⋮ A note on the complete Kähler-Einstein metrics of disk bundles over compact homogeneous Kähler manifolds ⋮ Moser-Trudinger type inequalities for complex Monge-Ampère operators and Aubin's ``hypothèse fondamentale ⋮ Positivity of direct images of positively curved volume forms ⋮ The volume of singular Kähler–Einstein Fano varieties ⋮ The volume of Kähler-Einstein Fano varieties and convex bodies ⋮ A Schwarz lemma for Kähler affine metrics and the canonical potential of a proper convex cone ⋮ Minimum principle for plurisubharmonic functions and related topics ⋮ Positivity of character subbundles and minimum principle for noncompact group actions ⋮ The spectral rigidity of complex projective spaces, revisited ⋮ Continuity of delta invariants and twisted Kähler-Einstein metrics ⋮ Lattice Point Inequalities for Centered Convex Bodies ⋮ Metric rigidity of Kähler manifolds with lower Ricci bounds and almost maximal volume ⋮ A volume stability theorem on toric manifolds with positive Ricci curvature ⋮ Variations of Minkowski's theorem on successive minima

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Real Monge-Ampère equations and Kähler-Ricci solitons on toric log Fano varieties
• The volume of Kähler-Einstein Fano varieties and convex bodies
• Examples of Kähler-Einstein toric Fano manifolds associated to non-symmetric reflexive polytopes
• Partitions of mass-distributions and of convex bodies by hyperplanes
• Plongements d'espaces homogènes
• When is a Schubert variety Gorenstein?
• Groupe de Picard et nombres caractéristiques des variétés sphériques. (Picard group and characteristic numbers of spheric varieties.)
• Obstructions to the existence of Sasaki-Einstein metrics
• A note on palindromic delta-vectors for certain rational polytopes
• Action d'une forme réelle d'un groupe de Lie complexe sur les fonctions plurisousharmoniques
• A special class of stationary flows for two-dimensional Euler equations: A statistical mechanics description
• The partial Legendre transformation for plurisubharmonic functions
• Note on the Hilbert polynomial of a spherical variety
• Equivariant completion
• A Riemannian interpolation inequality à la Borell, Brascamp and Lieb
• Yau-Tian-Donaldson correspondence for K-semistable Fano manifolds
• Bounds for the anticanonical bundle of a homogeneous projective rational manifold
• Kähler--Ricci solitons on toric manifolds with positive first Chern class
• Height and GIT weight
• Some theorems on actions of algebraic groups
• Curvature of vector bundles associated to holomorphic fibrations
• Kähler-Einstein metrics and the Kähler-Ricci flow on log Fano varieties
• Birational superrigidity and slope stability of Fano manifolds
• Reelle Transformationsgruppen und invariante Metriken auf komplexen Räumen
• On \(k\)-stability of reductive varieties
• Kähler-Einstein fillings
• Algebraic Equations and Convex Bodies
• Greatest lower bounds on the Ricci curvature of Fano manifolds
• Espaces Homogènes De Stein Des Groupes De Lie Complexes
• Kahler geometry on toric manifolds, and some other manifolds with large symmetry
• Kähler-Ricci solitons on homogeneous toric bundles
• Variétés horosphériques de Fano
• Convex bodies associated to linear series
• Calabi's conjecture and some new results in algebraic geometry
• Volume réticulaire critique d'un simplexe.
• Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties
• Marginals of Geometric Inequalities
• Higher-dimensional algebraic geometry
• Moser-Trudinger type inequalities for complex Monge-Ampère operators and Aubin's ``hypothèse fondamentale

This page was built for publication: The volume of Kähler-Einstein Fano varieties and convex bodies