• Corpus ID: 237563057

On the Bergman kernels of holomorphic vector bundles

  title={On the Bergman kernels of holomorphic vector bundles},
  author={L{\'a}szl{\'o} Lempert},
Consider a very ample line bundle E → X over a compact complex manifold, endowed with a hermitian metric of curvature −iω, and the space O(E) of its holomorphic sections. The Fubini–Study map associates with positive definite inner products 〈 , 〉 on O(E) functions FS(〈 , 〉) ∈ Hω = {u ∈ C∞(X) : ω + i∂∂u > 0}. We prove that FS is an injective immersion, but its image in general is not closed in Hω. To obtain a closed range, FS has to be extended to certain degenerate inner products. This we do by… 

On the metric structure of section ring

. The main goal of this article is to study for a projective manifold and an ample line bundle over it the relation between metric and algebraic structures on the associated section ring. More



Mapping properties of the Hilbert and Fubini–Study maps in Kähler geometry

Suppose that we have a compact Kahler manifold $X$ with a very ample line bundle $\mathcal{L}$. We prove that any positive definite hermitian form on the space $H^0 (X,\mathcal{L})$ of holomorphic

The Bergman Kernel and a Theorem of Tian

Given a domain Ω in ℂn, the Bergman kernel is the kernel of the projection operator from L 2 (Ω) to the Hardy space A 2 (Ω). When the boundary of Ω is strictly pseudoconvex and smooth, Fefferman [2]

Szego kernels and a theorem of Tian

We give 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. The proof is based on the

A Wess--Zumino--Witten type equation in the space of Kähler potentials in terms of Hermitian--Yang--Mills metrics

We prove that the solution of a Wess-Zumino-Witten type equation from a domain $D$ in $\mathbb{C}^m$ to the space of Kahler potentials can be approximated uniformly by Hermitian-Yang-Mills metrics on

On a set of polarized Kähler metrics on algebraic manifolds

A projective algebraic manifold M is a complex manifold in certain projective space CP, N > dim c M = n . The hyperplane line bundle of CP restricts to an ample line bundle L on M. This bundle L is a

Nonlinear analysis in geometry, L’Enseignement Math

  • 1987

extremality, interpolation of norms, and Kähler quantization, arXiv:1910.01782

  • 1910