表示的参数化变体的层次结构
A hierarchy of parametrizing varieties for representations
摘要：
主要目的是介绍和探讨投射簇$\text{GRASS}_{\bf d}(Λ)$，参数化有限维代数$Λ$上具有维数向量$\bf d$的那些模的全部集合。这些品种扩大了较小的品种以前研究的作者，即，投影品种编码这些模块与维数向量$\bf d$，此外，有一个预先指定的顶部或激进的分层。每一个$\text{GRASS}_{\bf d}(Λ)$又被线性代数群的作用所分割，并被某些表示理论定义的仿射子簇所覆盖，这些子簇在作用群的幂幺根下是稳定的。相关定理的一个特例是巴布森、托马斯和作者关于一般表示的工作的基石。此外，还介绍了其在简并研究中的应用。
英文摘要：
The primary purpose is to introduce and explore projective varieties, $\text{GRASS}_{\bf d}(Λ)$, parametrizing the full collection of those modules over a finite dimensional algebra $Λ$ which have dimension vector $\bf d$. These varieties extend the smaller varieties previously studied by the author; namely, the projective varieties encoding those modules with dimension vector $\bf d$ which, in addition, have a preassigned top or radical layering. Each of the $\text{GRASS}_{\bf d}(Λ)$ is again partitioned by the action of a linear algebraic group, and covered by certain representation-theoretically defined affine subvarieties which are stable under the unipotent radical of the acting group. A special case of the pertinent theorem served as a cornerstone in the work on generic representations by Babson, Thomas, and the author. Moreover, applications are given to the study of degenerations.
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