Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
157 tokens/sec
GPT-4o
8 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Off-diagonal decay of toric Bergman kernels (1603.08281v1)

Published 28 Mar 2016 in math.CV

Abstract: We study the off-diagonal decay of Bergman kernels $\Pi_{hk}(z,w)$ and Berezin kernels $P_{hk}(z,w)$ for ample invariant line bundles over compact toric projective \kahler manifolds of dimension $m$. When the metric is real analytic, $P_{hk}(z,w) \simeq km \exp - k D(z,w)$ where $D(z,w)$ is the diastasis. When the metric is only $C{\infty}$ this asymptotic cannot hold for all $(z,w)$ since the diastasis is not even defined for all $(z,w)$ close to the diagonal. We prove that for general $C{\infty}$ metrics, $P_{hk}(z,w) \simeq km \exp - k D(z,w)$ as long as $w$ lies on the ${\mathbb R}+m$-orbit of $z$, and for general $(z,w)$, $\limsup{k \to \infty} \frac{1}{k} \log P_{hk}(z,w) \leq - D(z,w^)$ where $D(z, w*)$ is the diastasis between $z$ and the translate of $w$ by $(S1)m$ to the ${\mathbb R}_+m$ orbit of $z$, complementary to Mike Christ's negative results (arXiv:1308.5644).

Summary

We haven't generated a summary for this paper yet.