Weighted Bergman Kernels on Orbifolds
Julius Ross,Richard P. Thomas +1 more
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A notion of ampleness for line bundles on orbifolds with cyclic quotient singularities that is related to embeddings in weighted projective space was introduced in this paper.Abstract:
We describe a notion of ampleness for line bundles on orbifolds with cyclic quotient singularities that is related to embeddings in weighted projective space, and prove a global asymptotic expansion for a weighted Bergman kernel associated to such a line bundle.read more
Citations
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Weighted projective embeddings, stability of orbifolds, and constant scalar curvature Kähler metrics
Julius Ross,Richard P. Thomas +1 more
TL;DR: In this paper, the existence of an orbifold Kahler metric of constant scalar curvature implies K-semistability, which is known as the GIT problem.
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A Closed Formula for the Asymptotic Expansion of the Bergman Kernel
TL;DR: In this paper, a graph theoretic closed formula for coefficients in the Tian-Yau-Zelditch asymptotic expansion of the Bergman kernel is presented, expressed in terms of the characteristic polynomial of the directed graphs representing Weyl invariants.
Journal ArticleDOI
A closed formula for the asymptotic expansion of the Bergman kernel
TL;DR: In this paper, a graph theoretic closed formula for coefficients in the Tian-Yau-Zelditch asymptotic expansion of the Bergman kernel is presented, expressed in terms of the characteristic polynomial of the directed graphs representing Weyl invariants.
Posted Content
Weighted projective embeddings, stability of orbifolds and constant scalar curvature K\"ahler metrics
J. Ross,R. P. Thomas +1 more
TL;DR: In this paper, the existence of an orbifold Kahler metric of constant scalar curvature implies K-semistability, which is known as the GIT problem.
Journal ArticleDOI
Asymptotics of Partial Density Functions for Divisors.
Julius Ross,Michael A. Singer +1 more
TL;DR: It is proved that this partial density function associated to sections of a positive hermitian line bundle that vanish to a particular order along a fixed divisor Y has a distributional asymptotic expansion that is in fact smooth upon passing to a suitable real blow-up.
References
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Journal ArticleDOI
Scalar Curvature and Projective Embeddings, I
TL;DR: In this article, it was shown that a metric of constant scalar curvature on a polarised Kahler manifold is the limit of metrics induced from a specific sequence of projective embeddings.
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The Bergman kernel and biholomorphic mappings of pseudoconvex domains
Journal ArticleDOI
On a set of polarized Kähler metrics on algebraic manifolds
TL;DR: In this paper, a projective algebraic manifold M is a complex manifold in certain projective space CP, N > dim c M = n, and the hyperplane line bundle of CP restricts to an ample line bundle L on M. This bundle L is a polarization on M, and it can be associated with a positive, rf-closed (1, l)-form ωg.
Book
Holomorphic Morse Inequalities and Bergman Kernels
Xiaonan Ma,George Marinescu +1 more
TL;DR: Demailly's Holomorphic Morse Inequalities on non-compact manifolds and the Bergman Kernel on noncompact manifold have been studied in this paper, where they have been shown to have similar properties to those of the Moishezon manifold.
Journal ArticleDOI
Szegö Kernels and a Theorem of Tian
TL;DR: In this article, a simple proof of Tian's theorem that the Kodaira embeddings associated to a positive line bundle over a compact complex manifold are asymptotically isometric was given.