HILBERT FUNCTIONS
HILBERT FUNCTIONS
复制标题
希尔伯特函数
DOI：
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发表时间：
2008
期刊：
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通讯作者：
Jordan Schettler
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文献类型：
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作者：
Jordan Schettler
希尔伯特函数(就我们将要讨论的而言)是从非负整数到它们自身的映射，它记录了分级模块中每一层的组成序列的长度。在许多感兴趣的情况下，附加到模上的希尔伯特函数与称为希尔伯特多项式的多项式在足够大的输入下一致。因此，无限数量的信息被编码在有限的对象中。事实上，希尔伯特多项式的次数和系数代表了重要的不变量，人们可以从这些不变量中读出模的性质。
A Hilbert function (so far as we will discuss) is a map from the nonnegative integers to themselves which records the lengths of composition series of each layer in a graded module. In many situations of interest, the Hilbert function attached to a module agrees for sufficiently large inputs with a polynomial, called a Hilbert polynomial. Thus an infinite amount of information is encoded in a finite object. Indeed, the degree and coefficients of a Hilbert polynomial represent important invariants from which one can potentially read off properties of the module.