TY - JOUR

T1 - Bergman kernels and equidistribution for sequences of line bundles on Kähler manifolds

AU - Coman, Dan

AU - Lu, Wen

AU - Ma, Xiaonan

AU - Marinescu, George

N1 - Funding Information:
D. C. is partially supported by the Simons Foundation Grant 853088 and the NSF Grant DMS-2154273.W. L. supported by NSFC Nos. 11401232, 11871233.X. M. partially supported by NSFC No. 11829102, ANR-21-CE40-0016 and funded through the Institutional Strategy of the University of Cologne within the German Excellence Initiative.G. M. partially supported by the DFG funded projects SFB TRR 191 ‘Symplectic Structures in Geometry, Algebra and Dynamics’ (Project-ID 281071066 – TRR 191) and SPP 2265 ‘Random Geometric Systems’ (Project-ID 422743078).
Publisher Copyright:
© 2023 Elsevier Inc.

PY - 2023/2/1

Y1 - 2023/2/1

N2 - 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→+∞.

AB - 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→+∞.

KW - Approximation of currents by analytic sets

KW - Bergman kernel

KW - Non-integral Kähler metric

KW - Zeros of random holomorphic sections

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U2 - 10.1016/j.aim.2022.108854

DO - 10.1016/j.aim.2022.108854

M3 - Article

AN - SCOPUS:85147559047

SN - 0001-8708

VL - 414

JO - Advances in Mathematics

JF - Advances in Mathematics

M1 - 108854

ER -