摘要翻译：
证明了arakelovian高度关于预对数-对数hermitian充裕线丛的下界和有限性质。这些高度是Burgos、Kramer和K\uhn在推广Gillet和Soul E的算术交集理论时引入的，旨在处理具有允许适当对数奇点的度量的hermitian向量丛。我们的结果推广了Bost-Gillet-Soul E高度的相应性质，以及Faltings对度量具有对数奇点的hermitian线丛上的点的高度所建立的性质。我们还讨论了这种预对数对数hermitian丰满线丛自然产生的各种几何构造。
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英文标题：
《Heights and metrics with logarithmic singularities》
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作者：
Gerard Freixas i Montplet
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最新提交年份：
2007
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分类信息：

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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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：
  We prove lower bound and finiteness properties for arakelovian heights with respect to pre-log-log hermitian ample line bundles. These heights were introduced by Burgos, Kramer and K\"uhn, in their extension of the arithmetic intersection theory of Gillet and Soul\'e, aimed to deal with hermitian vector bundles equipped with metrics admitting suitable logarithmic singularities. Our results generalize the corresponding properties for the heights of Bost-Gillet-Soul\'e, as well as the properties established by Faltings for heights of points attached to hermitian line bundles whose metrics have logarithmic singularities. We also discuss various geometric constructions where such pre-log-log hermitian ample line bundles naturally arise.
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PDF链接：
https://arxiv.org/pdf/0704.1046