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

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 $c_1(L_p,h_p)$. We then apply this to study the asymptotic distribution of common zeros of random sequences of $m$-tuples of sections of $L_p$ as $p\to \infty$.

24 pages

References in corpus (2)

• Generalized Bergman kernels on symplectic manifolds
• On the asymptotic expansion of Bergman kernel