Bergman kernels and the pseudoeffectivity of relative canonical bundles
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Publication:955158
DOI10.1215/00127094-2008-054zbMath1181.32025arXivmath/0703344OpenAlexW2005095103MaRDI QIDQ955158
Publication date: 18 November 2008
Published in: Duke Mathematical Journal (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0703344
Integral representations; canonical kernels (Szeg?, Bergman, etc.) (32A25) Bundle convexity (32L15) Removable sets in pluripotential theory (32U30)
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Cites Work
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- Unnamed Item
- Unnamed Item
- On the extension of \(L^ 2\) holomorphic functions
- A numerical criterion for very ample line bundles
- Variation of Bergman metrics on Riemann surfaces
- Multiplier ideal sheaves and Kähler-Einstein metrics of positive scalar curvature
- Pluricanonical systems of projective varieties of general type. I
- Kodaira dimension of algebraic fiber spaces over curves
- On Kähler fiber spaces over curves
- Invariance of plurigenera
- A theorem of \(L^ 2\) extension of holomorphic sections of a Hermitian bundle
- Orbifolds, special varieties and classification theory.
- Siu's invariance of plurigenera: a one-tower proof
- Analytic inversion of adjunction: \(L^2\) extension theorems with gain
- Curvature of vector bundles associated to holomorphic fibrations
- Multiplier ideal sheaves in complex and algebraic geometry
- Pluricanonical systems of projective varieties of general type. II
- Pluricanonical systems on algebraic varieties of general type
- Boundedness of pluricanonical maps of varieties of general type
- Manifolds with ample canonical class
- On the invariance and the lower semi-continuity of plurigenera of algebraic varieties
- Restricted volumes and base loci of linear series
- Minimal models and the Kodaira dimension of algebraic fiber spaces.
- Subadjunction of log canonical divisors, II
- Singular hermitian metrics on vector bundles
- ON THE VOLUME OF A LINE BUNDLE
- A Takayama-type extension theorem
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