论文标题
关于投影空间中高空曲面线性系统的GIT稳定性
On the GIT stability of linear systems of hypersurfaces in projective space
论文作者
论文摘要
我们考虑了通过几何不变理论（GIT）在某些投影空间中对高曲面（固定程度）的线性系统（固定程度）进行分类的问题。我们提供了一个明确的标准，可以完全解决问题。作为一种应用，我们考虑了一些相关的几何示例，例如恢复的，例如，米兰达对平面立方体铅笔的GIT稳定性的描述。此外，我们完全描述了任何指数的Halphen铅笔的GIT稳定性。
We consider the problem of classifying linear systems of hypersurfaces (of a fixed degree) in some projective space up to projective equivalence via geometric invariant theory (GIT). We provide an explicit criterion that solves the problem completely. As an application, we consider a few relevant geometric examples recovering, for instance, Miranda's description of the GIT stability of pencils of plane cubics. Furthermore, we completely describe the GIT stability of Halphen pencils of any index.
