The metric geometry of singularity types

DOI10.1515/crelle-2020-0019zbMath1503.32029arXiv1909.00839OpenAlexW3079265523MaRDI QIDQ2121380

Tamás Darvas, Eleonora Di Nezza, Hoang Chinh Lu

Publication date: 4 April 2022

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

Full work available at URL: https://arxiv.org/abs/1909.00839

zbMATH Keywords

complex Monge-Ampère equationmultiplier ideal sheavesbig cohomology classfinite energy class

Mathematics Subject Classification ID

"Global+differential+geometry+of+Hermitian+and+K%C3%A4hlerian+manifolds"&go=Go Global differential geometry of Hermitian and Kählerian manifolds (53C55) "K%C3%A4hler+manifolds"&go=Go Kähler manifolds (32Q15) "Complex+Monge-Amp%C3%A8re+operators"&go=Go Complex Monge-Ampère operators (32W20) "Plurisubharmonic+functions+and+generalizations"&go=Go Plurisubharmonic functions and generalizations (32U05)

Related Items (20)

Geodesic distance and Monge-Ampére measures on contact sets ⋮ Complex Hessian equations with prescribed singularity on compact Kähler manifolds ⋮ Rooftop envelopes and residual plurisubharmonic functions ⋮ Mabuchi geometry of big cohomology classes ⋮ Quasi-monotone convergence of plurisubharmonic functions ⋮ Continuity method with movable singularities for classical complex Monge-Ampere equations ⋮ Concavity property of minimal \(L^2\) integrals with Lebesgue measurable gain. IV: Product of open Riemann surfaces ⋮ A complete metric topology on relative low energy spaces ⋮ The strong topology of \(\omega \)-plurisubharmonic functions ⋮ Volume of components of Lelong upper-level sets ⋮ Boundary points, minimal \(L^2\) integrals and concavity property \(V\): vector bundles ⋮ Continuity of Monge-Ampère potentials with prescribed singularities ⋮ Weak solutions to complex Hessian type equations in the class \(\mathcal{E}_{\phi}(X, \omega, m)\) ⋮ A relative Yau-Tian-Donaldson conjecture and stability thresholds ⋮ Differential geometry in the large (hybrid meeting). Abstracts from the workshop held July 4--10, 2021 (hybrid meeting) ⋮ Concavity property of minimal \(L^2\) integrals with Lebesgue measurable gain V-fibrations over open Riemann surfaces ⋮ Geodesic stability, the space of rays and uniform convexity in Mabuchi geometry ⋮ The closures of test configurations and algebraic singularity types ⋮ Comparison of Monge–Ampère capacities ⋮ Kähler-Einstein metrics with prescribed singularities on Fano manifolds

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A proof of Demailly's strong openness conjecture
• Degenerate complex Monge-Ampère equations
• Monge-Ampère equations in big cohomology classes
• A new capacity for plurisubharmonic functions
• The Mabuchi geometry of finite energy classes
• Effectiveness of Demailly's strong openness conjecture and related problems
• Fine topology, Šilov boundary, and \((dd^ c)^ n\)
• The Dirichlet problem for a complex Monge-Ampère equation
• Monotonicity of nonpluripolar products and complex Monge-Ampère equations with prescribed singularity
• Numerical characterization of the Kähler cone of a compact Kähler manifold
• Plurisubharmonic envelopes and supersolutions
• Convexity of the extended K-energy and the large time behavior of the weak Calabi flow
• The weighted log canonical threshold
• Analytic test configurations and geodesic rays
• From Monge-Ampère equations to envelopes and geodesic rays in the zero temperature limit
• Semi-continuity of complex singularity exponents and Kähler–Einstein metrics on Fano orbifolds
• Volume and capacity of sublevel sets of a Lelong class of plurisubharmonic functions
• The Openness Conjecture and Complex Brunn-Minkowski Inequalities
• On the Cohomology of Pseudoeffective Line Bundles
• Numerical dimension and a Kawamata–Viehweg–Nadel-type vanishing theorem on compact Kähler manifolds
• On regularization of plurisubharmonic functions on manifolds
• Modules of Square Integrable Holomorphic Germs
• On the singularity type of full mass currents in big cohomology classes
• ON THE VOLUME OF A LINE BUNDLE
• Divisorial Zariski decompositions on compact complex manifolds
• A variational approach to the Yau–Tian–Donaldson conjecture
• Monotonicity of non-pluripolar Monge-Ampere masses
• WEAK GEODESIC RAYS IN THE SPACE OF KÄHLER POTENTIALS AND THE CLASS

This page was built for publication: The metric geometry of singularity types