Positivity of holomorphic vector bundles in terms of \(L^p\)-estimates for \(\bar{\partial}\)

DOI10.1007/s00208-021-02348-7OpenAlexW4206268313MaRDI QIDQ2697569

Jia Fu Ning, Zhi-Wei Wang, Xiang-Yu Zhou, Fu Sheng Deng

Publication date: 12 April 2023

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00208-021-02348-7

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Continuation of analytic objects in several complex variables (32D15) Other complex differential geometry (53C56) (overlinepartial) and (overlinepartial)-Neumann operators (32W05) Transcendental methods, Hodge theory (algebro-geometric aspects) (14C30) Holomorphic bundles and generalizations (32L05) Transcendental methods of algebraic geometry (complex-analytic aspects) (32J25) Plurisubharmonic functions and generalizations (32U05)

Related Items (4)

On the positivity of direct image bundles ⋮ Recent progress in the theory of functions of several complex variables and complex geometry ⋮ Bogomolov-Sommese type vanishing theorem for holomorphic vector bundles equipped with positive singular Hermitian metrics ⋮ New properties of multiplier submodule sheaves

Cites Work

• Unnamed Item
• Unnamed Item
• Suita conjecture and the Ohsawa-Takegoshi extension theorem
• A proof of Demailly's strong openness conjecture
• On the extension of \(L^ 2\) holomorphic functions
• Optimal constant problem in the \(L^2\) extension theorem
• Subharmonicity properties of the Bergman kernel and some other functions associated to pseudoconvex domains
• Bergman kernels and the pseudoeffectivity of relative canonical bundles
• A theorem of \(L^ 2\) extension of holomorphic sections of a Hermitian bundle
• An optimal \(L^2\) extension theorem on weakly pseudoconvex Kähler manifolds
• Ohsawa-Takegoshi extension theorem for compact Kähler manifolds and applications
• Complex geometry. An introduction
• Optimal constant in an \(L^2\) extension problem and a proof of a conjecture of Ohsawa
• Linear invariants of complex manifolds and their plurisubharmonic variations
• Siu's lemma, optimal \(L^2\) extension and applications to twisted pluricanonical 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
• Strong openness of multiplier ideal sheaves and optimal \(L^{2}\) extension
• Direct images, fields of Hilbert spaces, and geometric quantization
• Curvatures of direct image sheaves of vector bundles and applications
• \(L^ 2\) estimates and existence theorems for the \(\partial\)-operator
• On the extension of L² holomorphic functions V-Effects of generalization
• Positivity of twisted relative pluricanonical bundles and their direct images
• Hodge metrics and the curvature of higher direct images
• Algebraic fiber spaces over abelian varieties: Around a recent theorem by Cao and Păun
• Estimations $\mathrm{L}^2$ pour l'opérateur $\bar \partial$ d'un fibré vectoriel holomorphe semi-positif au-dessus d'une variété kählérienne complète
• L² Approaches in Several Complex Variables

This page was built for publication: Positivity of holomorphic vector bundles in terms of \(L^p\)-estimates for \(\bar{\partial}\)