A Variant of Weyl’s Inequality for Systems of Forms and Applications
A Variant of Weyl’s Inequality for Systems of Forms and Applications
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形式和应用系统的韦尔不等式的一个变体
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
D. Schindler
中科院分区：
文献类型：
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作者：
D. Schindler
我们给出了形式系统的Weyl不等式的一个变形及其应用。首先，我们用它来给出B.J.Birch关于多元形式的一个定理的另一种表述。更确切地说，我们证明了在给定形式的线性系统中，可以用形式的奇异轨迹的最大维来代替本文所引入的轨迹V∗的维度。在某些情况下，这改进了前面提到的Birch定理。
We give a variant of Weyl’s inequality for systems of forms together with applications. First we use this to give a different formulation of a theorem of B.J. Birch on forms in many variables. More precisely, we show that the dimension of the locus V∗ introduced in this work can be replaced by the maximal dimension of the singular loci of forms in the linear system of the given forms. In some cases this improves on the aforementioned theorem of Birch.