Recent progress in the theory of functions of several complex variables and complex geometry

DOI10.1134/s0040577924010112OpenAlexW4391453593MaRDI QIDQ6121934

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Publication date: 26 March 2024

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0040577924010112

zbMATH Keywords

stabilityholomorphic vector bundlesmultiplier idealstrong opennessconverse \(L^2\) theorysingular Nakano semipositive metricsubmodule sheaf

Mathematics Subject Classification ID

Sheaves and cohomology of sections of holomorphic vector bundles, general results (32L10) Plurisubharmonic functions and generalizations (32U05)

Cites Work

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• A proof of Demailly's strong openness conjecture
• Continuity properties of certain weighted log canonical thresholds
• On the extension of \(L^ 2\) holomorphic functions
• A numerical criterion for very ample line bundles
• Optimal constant problem in the \(L^2\) extension theorem
• Multiplier ideal sheaves and Kähler-Einstein metrics of positive scalar curvature
• Subharmonicity properties of the Bergman kernel and some other functions associated to pseudoconvex domains
• Effectiveness of Demailly's strong openness conjecture and related problems
• Valuations and plurisubharmonic singularities
• Bergman kernels and the pseudoeffectivity of relative canonical bundles
• On matrix Reinhardt domains
• Prekopa's theorem and Kiselman's minimum principle for plurisubharmonic functions
• Valuations and asymptotic invariants for sequences of ideals
• Optimal constant in an \(L^2\) extension problem and a proof of a conjecture of Ohsawa
• Stability of multiplier ideal sheaves
• Optimal \(L^2\) extension of sections from subvarieties in weakly pseudoconvex manifolds
• Characterizations of plurisubharmonic functions
• A converse of Hörmander's \(L^2\)-estimate and new positivity notions for vector bundles
• A solution of an \(L^{2}\) extension problem with an optimal estimate and applications
• Curvature of vector bundles associated to holomorphic fibrations
• \(L^ 2\) estimates and existence theorems for the \(\partial\)-operator
• Valuative analysis of planar plurisubharmonic functions
• Positivity of holomorphic vector bundles in terms of \(L^p\)-estimates for \(\bar{\partial}\)
• Semi-continuity of complex singularity exponents and Kähler–Einstein metrics on Fano orbifolds
• Numerical dimension and a Kawamata–Viehweg–Nadel-type vanishing theorem on compact Kähler manifolds
• Positivity of twisted relative pluricanonical bundles and their direct images
• A proof of the extended future tube conjecture
• Modules of Square Integrable Holomorphic Germs
• Valuations and multiplier ideals
• Algebraic fiber spaces over abelian varieties: Around a recent theorem by Cao and Păun
• Nakano positivity of singular Hermitian metrics and vanishing theorems \n of Demailly–Nadel–Nakano type
• K‐Stability and Kähler‐Einstein Metrics
• Kähler-Einstein metrics on Fano manifolds. I: Approximation of metrics with cone singularities
• A subadditivity property of multiplier ideals.

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