A converse of Hörmander's \(L^2\)-estimate and new positivity notions for vector bundles

DOI10.1007/s11425-019-1654-9zbMath1478.32063arXiv1901.02223OpenAlexW3016567152MaRDI QIDQ2238492

Takahiro Inayama, Genki Hosono

Publication date: 1 November 2021

Published in: Science China. Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.02223

zbMATH Keywords

singular Hermitian metrics\(L^2\)-estimateOhsawa-Takegoshi \(L^2\)-extension theorem

Mathematics Subject Classification ID

(overlinepartial) and (overlinepartial)-Neumann operators (32W05) Sheaves and cohomology of sections of holomorphic vector bundles, general results (32L10) Bundle convexity (32L15)

Related Items (7)

SINGULAR HERMITIAN METRICS WITH ISOLATED SINGULARITIES ⋮ From Hörmander's \(L^2\)-estimates to partial positivity ⋮ 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 ⋮ Positivity of holomorphic vector bundles in terms of \(L^p\)-estimates for \(\bar{\partial}\) ⋮ Holomorphic invariants of bounded domains ⋮ A remark on characterizations of Griffiths positivity through asymptotic conditions

Cites Work

• Positivity of direct images of positively curved volume forms
• Singular Hermitian metrics on holomorphic vector bundles
• Bergman kernels and the pseudoeffectivity of relative canonical bundles
• Prekopa's theorem and Kiselman's minimum principle for plurisubharmonic functions
• Approximations and examples of singular Hermitian metrics on vector bundles
• Positivity of twisted relative pluricanonical bundles and their direct images
• Algebraic fiber spaces over abelian varieties: Around a recent theorem by Cao and Păun
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