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Mathematics > Complex Variables

arXiv:2202.01638 (math)
[Submitted on 3 Feb 2022 (v1), last revised 13 Jun 2022 (this version, v2)]

Title:Limit of Bergman kernels on a tower of coverings of compact Kähler manifolds

Authors:Sungmin Yoo, Jihun Yum
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Abstract:We prove the convergence of the Bergman kernels and the $L^2$-Hodge numbers on a tower of Galois coverings $\{X_j\}$ of a compact Kähler manifold $X$ converging to an infinite Galois (not necessarily universal) covering $\widetilde{X}$. We also show that, as an application, sections of canonical line bundle $K_{X_j}$ for sufficiently large $j$ give rise to an immersion into some projective space, if so do sections of $K_{\widetilde{X}}$.
Subjects: Complex Variables (math.CV); Differential Geometry (math.DG)
Cite as: arXiv:2202.01638 [math.CV]
  (or arXiv:2202.01638v2 [math.CV] for this version)
  https://doi.org/10.48550/arXiv.2202.01638

Submission history

From: Sungmin Yoo [view email]
[v1] Thu, 3 Feb 2022 15:27:58 UTC (17 KB)
[v2] Mon, 13 Jun 2022 04:52:38 UTC (17 KB)
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