摘要翻译：
设X是赋有一个大线丛L的紧致复流形，我们将加权子集平衡时的能量定义为相关的极值复三次谐波权的Monge-Ampere能量。证明了平衡态能量相对于重量的可微性，并证明了该能量描述了KL整体截面空间中诱导超范数单位球体积k到无穷大时的渐近性态。作为这些结果的结果，我们推广了Rumely关于超限直径的Robin型公式。我们还得到了解析扭转的渐近描述，并将小高度代数点的袁氏等分布定理推广到大线丛的情形。
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英文标题：
《Growth of balls of holomorphic sections and energy at equilibrium》
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作者：
Robert Berman, Sebastien Boucksom
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最新提交年份：
2010
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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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一级分类：Mathematics        数学
二级分类：Number Theory        数论
分类描述：Prime numbers, diophantine equations, analytic number theory, algebraic number theory, arithmetic geometry, Galois theory
素数，丢番图方程，解析数论，代数数论，算术几何，伽罗瓦理论
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英文摘要：
  Let X be a compact complex manifold endowed with a big line bundle L. We define the energy at equilibrium of a weighted subset as the Monge-Ampere energy of the associated extremal plurisubharmonic weight. We prove the differentiability of the energy at equilibrium with respect to the weight, and show that this energy describes the asymptotic behaviour as k goes to infinity of the volume of the induced sup-norm unit ball in the space of global sections of kL. As a consequence of these results, we extend Rumely's Robin-type formula for the transfinite diameter. We also obtain an asymptotic description of the analytic torsion and extend Yuan's equidistribution theorem for algebraic points of small height to the case of a big line bundle.
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PDF链接：
https://arxiv.org/pdf/0803.1950