本质约化Hilbert模II
Essentially Reductive Hilbert Modules II
摘要：
m元多项式环上的许多Hilbert模本质上是可约的，即它们的扩张子是紧的。Arveson提出了齐次理想的闭包是否继承这个性质的问题，并提供了寻求肯定答案的动机。Arveson，Guo，Wang和作者都得到了肯定的结果。最近，郭和王将结果扩展到两个变量的准齐次理想。在此基础上，本文将这一结果推广到某些Reinhardt域上的Hilbert模，如二元椭球，并分析了当零簇维数为1时，将这一结果推广到m元拟齐次理想的闭包.
英文摘要：
Many Hilbert modules over the polynomial ring in m variables are essentially reductive, that is, have commutators which are compact. Arveson has raised the question of whether the closure of homogeneous ideals inherit this property and provided motivation to seek an affirmative answer. Positive results have been obtained by Arveson, Guo, Wang and the author. More recently, Guo and Wang extended the results to quasi-homogeneous ideals in two variables. Building on their techniques, in this note the author extends this result to Hilbert modules over certain Reinhardt domains such as ellipsoids in two variables and analyzes extending the result to the closure of quasi-homogeneous ideals in m variables when the zero variety has dimension one.
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