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摘要翻译：
设$L$是维数为$N,$的紧致复流形$X$上的全纯线丛，设$E^{-\phi}$是$L上的连续度量。$在$X$上固定测度$D\mu$给出了由$L的张量幂的全纯截面组成的Hilbert空间序列。$我们证明了相应的标度Bergman测度序列收敛，在高张量幂极限下，对$(K,\phi)的平衡测度，$,其中$K$是$d\mu的支持，只要$d\mu$对于$(K,\phi)是稳定的Bernstein-Markov,这里的Bergman测度表示$d\mu$乘以对应的正交投影算子的点态范数对角的限制。特别地，将有关随机矩阵和经典正交多项式的结果推广到高维。
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英文标题：
《Convergence of Bergman measures for high powers of a line bundle》
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作者：
Robert Berman and David Witt Nystrom
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最新提交年份：
2008
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分类信息：
一级分类：Mathematics 数学
二级分类：Complex Variables 复变数
分类描述：Holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves
全纯函数，自守群作用与形式，伪凸性，复几何，解析空间，解析束
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一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
Let $L$ be a holomorphic line bundle on a compact complex manifold $X$ of dimension $n,$ and let $e^{-\phi}$ be a continuous metric on $L.$ Fixing a measure $d\mu$ on $X$ gives a sequence of Hilbert spaces consisting of holomorphic sections of tensor powers of $L.$ We prove that the corresponding sequence of scaled Bergman measures converges, in the high tensor power limit, to the equilibrium measure of the pair $(K,\phi),$ where $K$ is the support of $d\mu,$ as long as $d\mu$ is stably Bernstein-Markov with respect to $(K,\phi).$ Here the Bergman measure denotes $d\mu$ times the restriction to the diagonal of the pointwise norm of the corresponding orthogonal projection operator. In particular, an extension to higher dimensions is obtained of results concerning random matrices and classical orthogonal polynomials.
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PDF链接：
https://arxiv.org/pdf/0805.2846
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