We look at coherent systems for decorated vector bundles and propose a notion of semistability. In the special case of tensor powers, we will study this notion more closely by doing some non-trivial constructions and computations in geometric invariant theory. It is an interesting aspect that ampleness of the linearization in the geometric invariant theory construction yields a bound on the stability parameter for coherent systems.

中文翻译：

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相干系统的一般概念

我们着眼于装饰矢量束的相干系统，并提出了半稳定性的概念。在张量幂的特殊情况下，我们将通过在几何不变理论中进行一些非平凡的构造和计算来更仔细地研究这个概念。一个有趣的方面是，几何不变理论构造中线性化的充分性对相干系统的稳定性参数产生了界限。