论文标题
平面中无序点的模量空间的稳定性变化
Variation of stability for moduli spaces of unordered points in the plane
论文作者
论文摘要
我们通过其相应的希尔伯特方案的GIT商的变化来研究平面中无序点的模量空间的压缩。我们的VGIT认为在充足的圆锥体外和可移动锥内的线性化。为此，我们将希尔伯特计划的描述用作莫里梦想空间，以及通过Bridgeland稳定性对其男子式模型的解释。我们确定与光滑圆锥上支持的曲线零维方案，界点和方案相关的GIT壁。在七个点中，我们研究了与可移动锥极端射线相关的紧凑型，稳定性与Chow商的行为差异很大。最后，给出了五个点的完整描述。
We study compactifications of the moduli space of unordered points in the plane via variation of GIT quotients of their corresponding Hilbert scheme. Our VGIT considers linearizations outside the ample cone and within the movable cone. For that purpose, we use the description of the Hilbert scheme as a Mori dream space, and the moduli interpretation of its birational models via Bridgeland stability. We determine the GIT walls associated with curvilinear zero-dimensional schemes, collinear points, and schemes supported on a smooth conic. For seven points, we study a compactification associated with an extremal ray of the movable cone, where stability behaves very differently from the Chow quotient. Lastly, a complete description for five points is given.
