Asymptotics for Bergman-Hodge kernels for high powers of complex line bundles

DOI10.5802/afst.1165zbMath1207.32012arXivmath/0511158OpenAlexW2062063419MaRDI QIDQ954076

Johannes Sjöstrand, Robert J. Berman

Publication date: 7 November 2008

Published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0511158

zbMATH Keywords

Bergman kernelDolbeault cohomology group

Mathematics Subject Classification ID

Sheaves and cohomology of sections of holomorphic vector bundles, general results (32L10) Geometric quantization (53D50) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Perturbations of PDEs on manifolds; asymptotics (58J37)

Related Items

Asymptotic expansion of the Bergman kernel via semi-classical symbolic calculus, Semi-classical asymptotics of Bergman and spectral kernels for $(0,q)$-forms, The second coefficient of the asymptotic expansion of the Bergman kernel of the Hodge-Dolbeault operator

Cites Work

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• The spin\(^{\mathbf c}\) Dirac operator on high tensor powers of a line bundle
• Bergman kernels and local holomorphic Morse inequalities
• Homogeneous vector bundles
• On a set of polarized Kähler metrics on algebraic manifolds
• A direct approach to Bergman kernel asymptotics for positive line bundles
• Autour de l'approximation semi-classique. (Around semiclassical approximation)
• Demailly's asymptotic Morse inequalities: a heat equation proof
• The eigenvalues of hypoelliptic operators. III: The non-semibounded case
• On the eigenvalues of a class of hypoelliptic operators
• Canonical coordinates and Bergmann metrics
• Pseudo-Kähler quantization on flag manifolds
• Symplectic submanifolds and almost-complex geometry
• Berezin--Toeplitz operators, a semi-classical approach
• Quantum monodromy and semi-classical trace formulæ.
• Universality and scaling of correlations between zeros on complex manifolds
• The log term of the Szegö kernel
• Convergence de la mêtrique de Fubini-Study d'un fibré linéaire positif. (Convergence of the Fubini-Study metric of a positive line bundle.)
• The Bergman kernel and biholomorphic mappings of pseudoconvex domains
• Lie algebra cohomology and the generalized Borel-Weil theorem
• Super Toeplitz operators on line bundles
• Determinants of pseudodifferential operators and complex deformations of phase space.
• Asymptotics of almost holomorphic sections of ample line bundles on symplectic manifolds
• Characteristic Classes and Homogeneous Spaces, I
• Asymptotic cohomological functions on projective varieties
• The Spectral Theory of Toeplitz Operators. (AM-99)
• Fourier integral operators with complex phase functions and parametrix for an interior boundary value problem
• On the lower order terms of the asymptotic expansion of Tian-Yau-Zelditch
• Semi-classical analysis for Harper's equation. III : Cantor structure of the spectrum
• THE FIRST COEFFICIENTS OF THE ASYMPTOTIC EXPANSION OF THE BERGMAN KERNEL OF THESpin^cDIRAC OPERATOR
• Generalized Bergman kernels on symplectic manifolds
• Parametrices for pseudodifferential operators with multiple characteristics
• On the asymptotic expansion of Bergman kernel