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摘要翻译：
设$K$是一个交换环，设$R$是一个交换的$K-$代数。本文的目的是定义和讨论与a（非必然交换的）$R-$代数的表示理论有关的图式之间的一些联系态射。$我们重点讨论了$A的$n-$维表示的方案$\ran//\gl_n$,$讨论了Hilbert方案$\hilb_a^n$参数化$A$的余维左理想的方案$\hilb_a^n$,以及$A上$n$阶除幂的仿射方案规范$\gamma_r^n(A)^{ab}$。$我们将Grothendieck-Deligne范数映射从$\hilb_a^n$推广到Spec$\gamma_r^n(a)^{ab}$,专门研究了当$a$是交换的且$k$是代数闭域时几何点上的Hilbert Chow态射。将Hilbert格式描述为一个主丛的基，我们将通过模空间$\ran//\gl_n$因子这个映射，给出这个Hilbert-Chow态射的一个很好的描述，从而证明它是射影的。
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英文标题：
《Hilbert-Chow morphism for non commutative Hilbert schemes and moduli
spaces of linear representations》
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作者：
Federica Galluzzi and Francesco Vaccarino
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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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一级分类：Mathematics 数学
二级分类：Representation Theory 表象理论
分类描述：Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra
代数和群的线性表示，李理论，结合代数，多重线性代数
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英文摘要：
Let $k$ be a commutative ring and let $R$ be a commutative $k-$algebra. The aim of this paper is to define and discuss some connection morphisms between schemes associated to the representation theory of a (non necessarily commutative) $R-$algebra $A. $ We focus on the scheme $\ran//\GL_n$ of the $n-$dimensional representations of $A, $ on the Hilbert scheme $\Hilb_A^n$ parameterizing the left ideals of codimension $n$ of $A$ and on the affine scheme Spec $\Gamma_R^n(A)^{ab} $ of the abelianization of the divided powers of order $n$ over $A. $ We give a generalization of the Grothendieck-Deligne norm map from $\Hilb_A^n$ to Spec $\Gamma_R^n(A)^{ab} $ which specializes to the Hilbert Chow morphism on the geometric points when $A$ is commutative and $k$ is an algebraically closed field. Describing the Hilbert scheme as the base of a principal bundle we shall factor this map through the moduli space $\ran//\GL_n$ giving a nice description of this Hilbert-Chow morphism, and consequently proving that it is projective.
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PDF链接：
https://arxiv.org/pdf/0808.3753
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