论文标题
Bridgeland稳定性歧管的局部紧凑型
A local compactification of the Bridgeland stability manifold
论文作者
论文摘要
Calabi-yau类别的稳定歧管在数学和物理学中都引起了人们的兴趣。通过查看一些已知的例子，一种模式清楚地出现了，并对它们的外观进行了相当精确的描述。特别是，它们似乎都缺失了基因座，这往往对应于球形物体上消失的退化稳定性条件。从镜像对称的角度来看，描述这种缺失的地层也很有趣，因为它们可以猜想地参数复杂结构的有趣类型。所有幼稚的尝试构建模块化的部分紧凑型的尝试表明，实际上是如何难以捉摸和微妙的问题：理想情况下，缺失的地层将对应于商三角形类别的稳定性歧管，但是在几何水平上建立这种对应关系，并在原始三角形类别上观看稳定性条件，这不是直接的稳定性条件的适当变性。在本文中，我们将提出一种方法，如果满足了一些其他障碍，则通过实现我们的兴趣空间作为稳定性歧管的合适度量完成，以构建这种部分压实。
Bridgeland stability manifolds of Calabi-Yau categories are of noticeable interest both in mathematics and in physics. By looking at some of the known example, a pattern clearly emerges and gives a fairly precise description of how they look like. In particular, they all seem to have missing loci, which tend to correspond to degenerate stability conditions vanishing on spherical objects. Describing such missing strata is also interesting from a mirror-symmetric perspective, as they conjecturally parametrize interesting types of degenerations of complex structures. All the naive attempts at constructing modular partial compactifications show how elusive and subtle the problem in fact is: ideally, the missing strata would correspond to stability manifolds of quotient triangulated categories, but establishing such correspondence on geometric level and viewing stability conditions on quotients of the original triangulated category as suitable degenerations of stability conditions is not straightforward. In this paper, we will present a method to construct such partial compactifications if some additional hypoteses are satisfied, by realizing our space of interest as a suitable metric completion of the stability manifold.
