We show that under very general assumptions the partial Bergman kernel function of sections vanishing along an analytic hypersurface has exponential decay in a neighborhood of the vanishing locus. Considering an ample line bundle, we obtain a uniform estimate of the Bergman kernel function associated to a singular metr…
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48 results for “partial Bergman kernels”
Estimates Bergman kernel for positive line bundles.
problem Estimating the Bergman kernel for positive line bundles.
method Explicit estimate using positive line bundles.
result Explicit lower bound of the Bergman kernel.
Semi-classical asymptotics of partial Bergman kernels on -symmetric complex manifolds with boundarymath.CV
The study examines Bergman kernels on complex manifolds with boundary and their asymptotic expansions.
problem Analyzing Bergman kernels on complex manifolds with boundary and their asymptotic behavior.
method Establishing asymptotic expansions of partial Bergman kernels for high-frequency Fourier modes on -symmetric complex manifolds with boundary.
result Established -equivariant extension results for biholomorphic maps between weakly pseudoconvex domains.
The study computes Bergman kernels and point process asymptotics on Kähler manifolds.
problem Computing asymptotics of Bergman kernels and point process distributions on Kähler manifolds.
method Equivariant and partial Bergman kernels, determinantal point processes, asymptotic analysis.
result The distribution of linear statistics converges to a centered normal variable with specific variances.
Sharp estimates for Bergman metrics derived from Kähler quantization.
problem Estimating Bergman metrics in Kähler quantization.
method Upper and lower bounds on the Bergman metric expressed in terms of .
result Optimal -convergence for quantization of Kähler currents.
Study Bergman kernels on complex hyperbolic cusps, generalizing previous results.
problem Localization of Bergman kernels on Kähler manifolds with complex hyperbolic cusps.
method Revisiting Tian's peak section method, applying to Kähler-Einstein metrics and quotients of complex balls.
result Partial localization result for Poincaré type cusps.
The study shows algebraic Bergman kernels imply finite type boundaries in complex domains.
problem Understanding the relationship between algebraic Bergman kernels and the finite type of boundaries in complex domains.
method Analyzing algebraic Bergman kernels and their implications on the finite type of boundaries in smoothly bounded pseudoconvex domains in .
result The boundary of a smoothly bounded pseudoconvex domain with an algebraic Bergman kernel of degree is of finite type with type .
The Bergman kernels of holomorphic vector bundles are studied to extend the Fubini-Study map.
problem Extending the Fubini-Study map to a closed range for general inner products.
method Associate Bergman kernels with general inner products on the dual space.
result FS is an injective immersion but not necessarily closed in the space of positive definite inner products.
The paper proves the existence of a special type of metric on complex manifolds.
problem Finding metrics with specific properties on complex manifolds.
method Proving the existence of n-complex dimensional manifolds with strictly partially regular and cscK metrics.
result For n ≥ 3, the (constant) scalar curvature of the metric can be zero, positive, or negative.
Formula for Bergman kernel of complex hyperbolic manifolds proved.
problem Calculating the Bergman kernel of complex hyperbolic manifolds.
method Expressed as a sum over geodesic loops.
result Maximum and minimum of the Bergman kernel function proved.
Study continuity of Bergman kernels on degenerating varieties.
problem Continuity and uniform convergence of Bergman kernels on degenerating varieties.
method Introduced fiberwise Bergman kernel for flat families of polarized varieties, established continuity and uniform convergence results.
result Uniform convergence of Fubini-Study currents and continuity of fiberwise Bergman kernel on test configurations.
The paper improves -estimates for Dirac-Dolbeault operators on complex manifolds.
problem Improving -estimates for Dirac-Dolbeault operators on complex manifolds.
method Generalized classical method to handle mixed curvature cases and provided bounds on error terms.
result Full asymptotic expansion for Bergman kernel obtained.
Study Bergman kernels on Kähler manifolds, answering Lu-Tian's question.
problem Understanding Bergman kernels on Kähler manifolds and their properties.
method Localization and expansion analysis of Bergman kernels.
result Answered Lu-Tian's question about Bergman kernels having no logarithmic singularity.
Explicit formula for Bergman kernel of abelian varieties proved.
problem Explicit formula for Bergman kernel of polarized abelian varieties.
method Explicit formula for Bergman kernel of polarized abelian varieties.
result Explicit formula for Bergman kernel of polarized abelian varieties.
Paper compares Bergman kernel and Masur-Veech measure on Teichmüller space.
problem Comparing Bergman kernel and Masur-Veech measure on Teichmüller space.
method Comparison between Bergman kernel form and pushforward measure of Masur-Veech measure.
result Obtained a comparison between the Bergman kernel form and the pushforward measure of the Masur-Veech measure.
We study the asymptotic behavior of the generalized Bergman kernel of the renormalized Bochner-Laplacian on high tensor powers of a positive line bundle on a symplectic manifold of bounded geometry. First, we establish the off-diagonal exponential estimate for the generalized Bergman kernel. As an application, we obtai…
In this paper, we survey some recent results about the asymptotic expansion of Bergman kernel and we give a Bergman kernel proof of Kodaira embedding theorem.
Unified proofs of weak holomorphic Morse inequalities using Bergman kernel functions.
problem Weak holomorphic Morse inequalities on various types of manifolds.
method Asymptotic Bergman kernel functions and Bochner-Kodaira-Nakano formulas.
result Unified proofs of weak holomorphic Morse inequalities.
New method for spectral and Bergman kernels under local spectral gap condition.
problem Analyzing spectral and Bergman kernels for complex manifolds.
method Developed a new scaling method to study spectral and Bergman kernels.
result Established pointwise asymptotics of spectral and Bergman kernels.
Study Bergman kernel metrics on degenerating hyperelliptic surfaces.
problem Asymptotic behavior of Bergman kernels near singularities.
method Taylor expansion for Abelian differentials and period matrices.
result Explicit coefficients in asymptotic formulas for Bergman kernels.
Relying on the recent work of Liu-Székelyhidi we give a weak asymptotic estimate for the Bergman kernels of polarized Kähler manifolds with Ricci lower bound and Sobolev constant upper bound. We will also give a simple proof for the partial estimate along the (generalized) Kähler-Ricci flow on Fano manifolds.
Inspired by Berndtsson's work on the subharmonicity property of the Bergman kernel, we give a local variation formula of the full Bergman kernels associated to deformations of complex manifolds. In compact case, it follows from the reproducing property of the Bergman kernel and the curvature formula of the 0-th direct …
Study shows Bergman kernel quotient approaches one for punctured surfaces.
problem Analyzing Bergman kernels on punctured Riemann surfaces.
method Examined a punctured Riemann surface with a specific metric and line bundle, calculating quotient of Bergman kernels.
result The quotient of Bergman kernels tends to one as tensor power increases.
The paper studies invariant weighted Bergman metrics on domains.
problem Investigating invariant weighted Bergman metrics under biholomorphisms.
method Introducing invariant weight assignments, using Bergman's minimum integral method and domain version of Tian-Yau-Zelditch expansion.
result Uniform convergence of weighted Bergman kernels and metrics on uniform squeezing domains.
Using the techniques developed in \cite{SunSun}, we give estimations of the Bergman kernel of the punctured disk with the standard complete Poincaré metric. As an application, we improve the result of \cite{AMM} on the Bergman kernels of punctured Riemann surfaces near singularities.
Toeplitz operators linked to submultiplicative filtrations and weighted Bergman kernels.
problem Analyzing the asymptotics of weighted Bergman kernels for submultiplicative filtrations.
method Demonstrated that weight operator is a Toeplitz operator; analyzed asymptotics of weighted Bergman kernels.
result Local refinement of convergence of jumping measures towards geodesic ray pushforward measure.
Study shows Bergman kernels match averages on quotient spaces, proving non-vanishing of Poincaré series.
problem Proving non-vanishing of Poincaré series on finite-volume quotients of Hermitian symmetric spaces.
method Using Bergman kernels and averaging over discrete groups, proving non-vanishing of Poincaré series.
result Large class of relative Poincaré series does not vanish on general locally symmetric spaces of finite volume.
We prove an exponential estimate for the asymptotics of Bergman kernels of a positive line bundle under hypotheses of bounded geometry. We give further Bergman kernel proofs of complex geometry results, such as separation of points, existence of local coordinates and holomorphic convexity by sections of positive line b…
In this paper we consider a punctured Riemann surface endowed with a Hermitian metric which equals the Poincaré metric near the punctures and a holomorphic line bundle which polarizes the metric. We show that the Bergman kernel can be localized around the singularities and its local model is the Bergman kernel of the p…
We establish the existence of the asymptotic expansion of the Bergman kernel associated to the spin-c Dirac operators acting on high tensor powers of line bundles with non-degenerate mixed curvature (negative and positive eigenvalues) by extending the paper " On the asymptotic expansion of Bergman kernel " (math.DG/040…
The Bergman kernel and period map for curves are studied.
problem Characterize the Torelli map's second fundamental form on the moduli space of curves.
method Use the Bergman kernel form associated to the curve and its harmonic representative.
result The Bergman kernel form is the harmonic representative of the multiplication by a certain meromorphic form.
We obtain several results about stability of the Bergman kernel on a tower of coverings on complex manifolds. An effective version of Rhodes' result is given for a tower of coverings on a compact Riemann surface of genus greater than or equal to 2. Stability of the Bergman kernel is established for towers of coverings …
The Bergman-Szegő kernel is analyzed for weakly pseudoconvex CR manifolds of finite type.
problem Analyzing the Bergman-Szegő kernel for specific CR manifolds.
method Constructing a parametrix for the Szegő kernel, extending earlier results.
result Extending Fefferman's boundary asymptotics to weakly pseudoconvex domains in \(\mathbb{C}^{2}\).
We give an alternate proof of the existence of the asymptotic expansion of the Bergman kernel associated to the -th tensor powers of a positive line bundle in a -neighborhood of the diagonal using elementary methods. We use the observation that after rescaling the Kähler potential …
Study shows convergence of Bergman kernels on covering spaces of Kähler manifolds.
problem Analyzing convergence of Bergman kernels on covering spaces of Kähler manifolds.
method Proving convergence of Bergman kernels and -Hodge numbers on a tower of coverings.
result Sections of canonical line bundles give rise to immersions into projective spaces.
Study equivalence of metrics on noncompact Kähler manifolds with Bergman kernel properties.
problem Equivalence of invariant metrics on noncompact Kähler manifolds with bounded curvature.
method Use boundedness of ratio between Bergman kernel and wedge product of metric in fundamental domain.
result Equivalence of Bergman metric and Kähler-Einstein metric under specific conditions.
We study the asymptotic of the Bergman kernel of the spin Dirac operator on high tensor powers of a line bundle.
Master thesis proves Bergman kernel asymptotics for positive line bundles.
problem Proving asymptotic expansion of Bergman kernel for positive line bundles.
method Introduced a semi-classical symbol space and symbolic calculus.
result Established pointwise asymptotic expansion on positive parts of certain semi-positive line bundles.
Quantizes semipositive line bundles on complex manifolds.
problem Quantize semipositive line bundles without ample representatives.
method Use adjoint Bergman kernels and non-pluripolar Monge-Ampère measures.
result Quantized energy converges to Monge-Ampère energy in semipositive setting.
The paper discusses convergence of Bergman kernels on complex manifolds.
problem Convergence of Bergman kernels on complex manifolds with given conditions.
method Analysis of Gromov-Hausdorff limits, Hermitian line bundles, and positive currents.
result Uniform asymptotic expansion and estimates of Bergman kernels.
We establish an asymptotic expansion for families of Bergman kernels. The key idea is to use the superconnection as in the local family index theorem.
Study Bergman kernels and zero distributions of random sections on Kähler manifolds.
problem Asymptotic distribution of common zeros of random sections on Kähler manifolds.
method Analysis of Bergman kernels and equidistribution for sequences of line bundles.
result Established asymptotic expansion of Bergman kernels and equidistribution of zeros.
Orbifold Bergman Kernelsmath.DG
Study Bergman kernels on Kähler orbifolds with specific properties.
problem Analyzing Bergman kernels on compact Kähler orbifolds.
method Examining weighted sums of Bergman kernels for specific vector bundles and metrics.
result Bergman kernels admit asymptotic expansions for certain conditions.
We provide a simple proof of a result of Rouby-Sjöstrand-Ngoc \cite{RSN} and Deleporte \cite{Deleporte}, which asserts that if the Kähler potential is real analytic then the Bergman kernel is an \textit{analytic kernel} meaning that its amplitude is an \textit{analytic symbol} and its phase is given by the polarization…
Study shows quantum behavior near infinity in metric asymptotics.
problem Quantum behavior of metrics near infinity on quasi-projective manifolds.
method Analysis of Bergman kernel function near smooth divisor at infinity of Cheng-Yau metric.
result Quantum phenomenon observed for points very close to the divisor at infinity.
In this paper, we study the behavior of Bergman kernels along the Kähler Ricci flow on Fano manifolds. We show that the Bergman kernels are equivalent along the Kähler Ricci flow under certain condition on the Ricci curvature of the initial metric. Then, using a recent work of Tian and Zhang, we can solve a conjecture …
Two-dimensional domains with Kähler-Einstein Bergman metrics are biholomorphic to the unit ball.
problem Characterizing domains with Kähler-Einstein Bergman metrics.
method Asymptotics of derivatives of the Bergman kernel along critically tangent paths.
result Two-dimensional pseudoconvex domains with Kähler-Einstein Bergman metrics are biholomorphic to the unit ball.
We give a version of the comparison principle from pluripotential theory where the Monge-Ampère measure is replaced by the Bergman kernel and use it to derive a maximum principle