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→+∞.
- Approximation of currents by analytic sets
- Bergman kernel
- Non-integral Kähler metric
- Zeros of random holomorphic sections
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