Plurisubharmonic geodesics in spaces of non-Archimedean metrics of finite energy

DOI10.1515/crelle-2022-0059OpenAlexW3112058058MaRDI QIDQ2100854

Rémi Reboulet

Publication date: 25 November 2022

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

Full work available at URL: https://arxiv.org/abs/2012.07972

Mathematics Subject Classification ID

Projective and enumerative algebraic geometry (14Nxx) Several complex variables and analytic spaces (32-XX)

Related Items

The existence of the Kähler–Ricci soliton degeneration ⋮ Global pluripotential theory over a trivially valued field ⋮ Convexity of multiplicities of filtrations on local rings ⋮ The space of finite-energy metrics over a degeneration of complex manifolds

Cites Work

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• Kiselman's principle, the Dirichlet problem for the Monge-Ampère equation, and rooftop obstacle problems
• Monge-Ampère equations in big cohomology classes
• The Mabuchi geometry of finite energy classes
• Growth of balls of holomorphic sections and energy at equilibrium
• Some symplectic geometry on compact Kähler manifolds. I
• The partial Legendre transformation for plurisubharmonic functions
• Maximally complete fields
• The space of Kähler metrics.
• Tropical and non-Archimedean limits of degenerating families of volume forms
• Distribution of logarithmic spectra of the equilibrium energy
• Geodesic stability, the space of rays and uniform convexity in Mabuchi geometry
• Spaces of norms, determinant of cohomology and Fekete points in non-Archimedean geometry
• Continuity of plurisubharmonic envelopes in non-Archimedean geometry and test ideals. With an appendix by José Ignacio Burgos Gil and Martín Sombra.
• Tropical varieties for non-archimedean analytic spaces
• Convexity of the extended K-energy and the large time behavior of the weak Calabi flow
• The Monge-Ampère operator and geodesics in the space of Kähler potentials
• Analytic test configurations and geodesic rays
• The asymptotic Fubini-Study operator over general non-Archimedean fields
• Singular semipositive metrics in non-Archimedean geometry
• La droite de Berkovich sur Z
• Complex Monge-Ampere and Symplectic Manifolds
• Extension property of semipositive invertible sheaves over a non-archimedean field
• Summary on non-Archimedean valued fields
• On the <scp>Yau‐Tian‐Donaldson</scp> Conjecture for Singular Fano Varieties
• Differentiability of Relative Volumes Over an Arbitrary Non-Archimedean Field
• Quantization in Geometric Pluripotential Theory
• A variational approach to the Yau–Tian–Donaldson conjecture
• Geometric pluripotential theory on Kähler manifolds
• Solution to a non-Archimedean Monge-Ampère equation
• Bruhat-Tits Buildings and Analytic Geometry
• Möbius orthogonality for generalized Morse-Kakutani flows
• Global pluripotential theory over a trivially valued field