论文标题
通过无质量的半含量物体对稳定性歧管的部分压实
Partial compactification of stability manifolds by massless semistable objects
论文作者
论文摘要
我们介绍了三角形类别的Bridgeland稳定性条件空间的两个部分压缩。首先，我们考虑允许允许半固定物体的质量为零但仍具有相位的宽松稳定性条件。无质量物体的子类别厚，并且商类别上有一个诱发的经典稳定性。我们研究松弛稳定性条件的变形。其次，我们考虑通过识别与固定电荷的变形 - 等效的松弛稳定性条件来产生的空间。第二个空间是由三角形类别的Verdier商的稳定空间分层的，该空间由无质量对象的厚子类别进行。我们通过示例将Grothendieck组的等级为2进行说明。对于这些，我们的部分紧凑型可以被明确描述，并与稳定空间的墙壁和室结构有关。
We introduce two partial compactifications of the space of Bridgeland stability conditions of a triangulated category. First we consider lax stability conditions where semistable objects are allowed to have mass zero but still have a phase. The subcategory of massless objects is thick and there is an induced classical stability on the quotient category. We study deformations of lax stability conditions. Second we consider the space arising by identifying lax stability conditions which are deformation-equivalent with fixed charge. This second space is stratified by stability spaces of Verdier quotients of the triangulated category by thick subcategories of massless objects. We illustrate our results through examples in which the Grothendieck group has rank 2. For these, our partial compactification can be explicitly described and related to the wall-and-chamber structure of the stability space.
