A general extension theorem for cohomology classes on non reduced analytic subspaces

DOI10.1007/s11425-017-9066-0zbMath1379.32017arXiv1703.00292OpenAlexW3103703404MaRDI QIDQ2400395

Jean-Pierre Demailly, Shin-ichi Matsumura, Junyan Cao

Publication date: 1 September 2017

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

Full work available at URL: https://arxiv.org/abs/1703.00292

zbMATH Keywords

singular Hermitian metricmultiplier ideal sheafOhsawa-Takegoshi extension theoremholomorphically convex Kähler manifold

Mathematics Subject Classification ID

Kähler manifolds (32Q15) Sheaves and cohomology of sections of holomorphic vector bundles, general results (32L10) Holomorphically convex complex spaces, reduction theory (32E05)

Related Items

On an \(L^2\) extension theorem from log-canonical centres with log-canonical measures ⋮ A pointwise norm on a non-reduced analytic space ⋮ \(L^2\) extensions with singular metrics on Kähler manifolds ⋮ Extension with log-canonical measures and an improvement to the plt extension of Demailly-Hacon-Păun ⋮ Regularization of quasi-plurisubharmonic functions on complex manifolds ⋮ Characterization of pseudo-effective vector bundles by singular Hermitian metrics ⋮ On the extension of holomorphic adjoint sections from reduced unions of strata of divisors ⋮ Norm estimates for the \(\bar{\partial}\)-equation on a non-reduced space ⋮ On asymptotic base loci of relative anti-canonical divisors of algebraic fiber spaces ⋮ Concavity property of minimal \(L^2\) integrals with Lebesgue measurable gain. IV: Product of open Riemann surfaces ⋮ \(L^2\) extension of holomorphic functions for log canonical pairs ⋮ On the Ohsawa-Takegoshi extension theorem ⋮ Boundary points, minimal \(L^2\) integrals and concavity property \(V\): vector bundles ⋮ Open problems on structure of positively curved projective varieties ⋮ Geometric methods of complex analysis. Abstracts from the workshop held May 16--22, 2021 (hybrid meeting) ⋮ Concavity property of minimal \(L^2\) integrals with Lebesgue measurable gain V-fibrations over open Riemann surfaces ⋮ Recent results in several complex variables and complex geometry ⋮ Injectivity theorem for pseudo-effective line bundles and its applications ⋮ On the global generation of direct images of pluri-adjoint line bundles ⋮ On weighted Bergman spaces of a domain with Levi-flat boundary ⋮ Extension of cohomology classes and holomorphic sections defined on subvarieties ⋮ \(L^2\) extension of \(\bar{\partial} \)-closed forms on weakly pseudoconvex Kähler manifolds

Cites Work

• Unnamed Item
• A proof of Demailly's strong openness conjecture
• On the extension of \(L^ 2\) holomorphic functions
• \(L^ 2\)-cohomology and index theorem for the Bergman metric
• \({\bar\partial}\)-cohomology of (H,C)-groups
• The weighted log canonical threshold
• On a curvature condition that implies a cohomology injectivity theorem of Kollár-Skoda type
• On the Cohomology of Pseudoeffective Line Bundles
• A transcendental approach to Kollár's injectivity theorem II
• An injectivity theorem with multiplier ideal sheaves of singular metrics with transcendental singularities
• Estimations $\mathrm{L}^2$ pour l'opérateur $\bar \partial$ d'un fibré vectoriel holomorphe semi-positif au-dessus d'une variété kählérienne complète
• PSEUDO-EFFECTIVE LINE BUNDLES ON COMPACT KÄHLER MANIFOLDS
• The Neumann Problem for the Cauchy-Riemann Complex. (AM-75)