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 -