Toric pluripotential theory

DOI10.4064/ap180409-3-7zbMath1439.32100arXiv1804.03387OpenAlexW2962815572WikidataQ129098741 ScholiaQ129098741MaRDI QIDQ5207251

Ahmed Zeriahi, Vincent Guedj, Sibel Sahin, Dan Coman

Publication date: 19 December 2019

Published in: Annales Polonici Mathematici (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.03387

zbMATH Keywords

Lelong numbertoric manifoldcomplex Monge-Ampère operatorDelzant polytopequasiplurisubharmonic function

Mathematics Subject Classification ID

Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Complex Monge-Ampère operators (32W20) Plurisubharmonic functions and generalizations (32U05) Lelong numbers (32U25) Capacity theory and generalizations (32U20)

Related Items (7)

Magnetic Geodesics on the Space of K\"ahler Potentials ⋮ Quasi-monotone convergence of plurisubharmonic functions ⋮ Dynamical tropicalisation ⋮ Conical Calabi-Yau metrics on toric affine varieties and convex cones ⋮ Singular Kähler-Einstein metrics on \(\mathbb{Q}\)-Fano compactifications of Lie groups ⋮ Multiplier Hermitian-Einstein metrics on Fano manifolds of KSM-type ⋮ Optimal transport on completely integrable toric manifolds

Cites Work

• Real Monge-Ampère equations and Kähler-Ricci solitons on toric log Fano varieties
• Monge-Ampère equations in big cohomology classes
• Some remarks on the symplectic and Kähler geometry of toric varieties
• A new capacity for plurisubharmonic functions
• The Mabuchi geometry of finite energy classes
• The Dirichlet problem for a complex Monge-Ampère equation
• Kaehler structures on toric varieties
• The Guillemin formula and Kähler metrics on toric symplectic manifolds
• The weighted Monge-Ampère energy of quasiplurisubharmonic functions
• Domains of definition of Monge-Ampère operators on compact Kähler manifolds
• Hamiltoniens périodiques et images convexes de l'application moment
• The Monge-Ampère equation
• Finite pluricomplex energy measures
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