Bergman kernels and equidistribution for sequences of line bundles on Kähler manifolds

Dan Coman, Wen Lu, Xiaonan Ma, George Marinescu

Research output: Contribution to journalArticlepeer-review

Abstract

Given a sequence of positive Hermitian holomorphic line bundles (Lp,hp) on a Kähler manifold X, we establish the asymptotic expansion of the Bergman kernel of the space of global holomorphic sections of Lp, under a natural convergence assumption on the sequence of curvatures c1(Lp,hp). We then apply this to study the asymptotic distribution of common zeros of random sequences of m-tuples of sections of Lp as p→+∞.

Original languageEnglish (US)
Article number108854
JournalAdvances in Mathematics
Volume414
DOIs
StatePublished - Feb 1 2023

Keywords

  • Approximation of currents by analytic sets
  • Bergman kernel
  • Non-integral Kähler metric
  • Zeros of random holomorphic sections

ASJC Scopus subject areas

  • General Mathematics

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