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arXiv · 2012.12019

Bergman kernels and equidistribution for sequences of line bundles on K\"ahler manifolds

Dan Coman·Wen Lu·Xiaonan Ma·George Marinescu
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Abstract

Given a sequence of positive Hermitian holomorphic line bundles $(L_p,h_p)$ on a K\"ahler 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 $c_1(L_p,h_p)$. We then apply this to study the asymptotic distribution of common zeros of random sequences of $m$-tuples of sections of $L_p$ as $p\to\infty$.

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BibTeXRIS

Dan Coman, Wen Lu, Xiaonan Ma, George Marinescu. 2020-12-22. Bergman kernels and equidistribution for sequences of line bundles on K\"ahler manifolds. https://arxiv.org/abs/2012.12019

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