有限维表示II的顶稳定退化
Top-stable degenerations of finite dimensional representations II
摘要：
设$Λ$是代数闭域上的有限维代数.我们展示切片的表示论的$Λ$，总是在严格的几何分类。也就是说，我们证明了，对于任何半单对象$T \in Λ\text{-mod}$，具有固定维数向量的$Λ$ -模（例如$\bf d$）和不允许任何真的顶稳定退化的顶$T$的类具有一个细模空间。这个模空间$\mathfrak{ModuliMax}^T_{\bf d}$是一个射影簇。尽管可分类性达到同构，但模块的目标集合在理论上是丰富的表示：实际上，任何投射变体都是作为$\mathfrak{ModuliMax}^T_{\bf d}$出现的，用于适当地选择$Λ$、$\bf d$和$T$。在串联，我们给出了一个结构表征的有限维表示，没有适当的顶稳定退化。
英文摘要：
Let $Λ$ be a finite dimensional algebra over an algebraically closed field. We exhibit slices of the representation theory of $Λ$ that are always classifiable in stringent geometric terms. Namely, we prove that, for any semisimple object $T \in Λ\text{-mod}$, the class of those $Λ$-modules with fixed dimension vector (say $\bf d$) and top $T$ which do not permit any proper top-stable degenerations possesses a fine moduli space. This moduli space, $\mathfrak{ModuliMax}^T_{\bf d}$, is a projective variety. Despite classifiability up to isomorphism, the targeted collections of modules are representation-theoretically rich: indeed, any projective variety arises as $\mathfrak{ModuliMax}^T_{\bf d}$ for suitable choices of $Λ$, $\bf d$, and $T$. In tandem, we give a structural characterization of the finite dimensional representations that have no proper top-stable degenerations.
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