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

2020/12/22 by Coman, Dan, Lu, Wen, Ma, Xiaonan +1 · 1 citation
#Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Probability (math.PR) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2012.12019

Abstract

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

Cited by

• Asymptotic Mass Distribution of Random Holomorphic Sections

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