摘要翻译：
给出了代数整数环谱上几个非零Hermitian向量丛张量积的最大斜率的一个上界。利用Minkowski定理，我们需要估计张量积的任意Hermitian线子丛的Arakelov度。在几何不变理论意义下，$M$的一般纤维是半可观测的情况下，通过经典不变理论构造一个在$M$的一般纤维上不消失的特殊多项式来建立估计。否则，我们使用Ramanan和Ramanathan的结果的一个明确版本来将一般情况简化为前一种情况。
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英文标题：
《Maximal slope of tensor product of Hermitian vector bundles》
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作者：
Huayi Chen (CMLS-EcolePolytechnique)
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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：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 give an upper bound for the maximal slope of the tensor product of several non-zero Hermitian vector bundles on the spectrum of an algebraic integer ring. By Minkowski's theorem, we need to estimate the Arakelov degree of an arbitrary Hermitian line subbundle $\bar M$ of the tensor product. In the case where the generic fiber of $M$ is semistable in the sense of geometric invariant theory, the estimation is established by constructing, through the classical invariant theory, a special polynomial which does not vanish on the generic fibre of $M$. Otherwise we use an explicte version of a result of Ramanan and Ramanathan to reduce the general case to the former one.
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PDF链接：
https://arxiv.org/pdf/0706.0690