Stability conditions on triangulated categories
Stability conditions on triangulated categories
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DOI：
10.4007/annals.2007.166.317
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发表时间：
2002-12
影响因子：
4.9
通讯作者：
T. Bridgeland
中科院分区：
文献类型：
--
作者：
T. Bridgeland
本文引入了三角化范畴上的稳定性条件的概念。动机来自于对弦理论中狄利克雷膜的研究，特别是来自于道格拉斯先生的$\Pi$稳定性的概念。从数学的角度来看，该定义最有趣的特征是，固定范畴$\T$上的稳定性条件$\Stab(\T)$具有自然拓扑，从而定义了三角化范畴的一个新的不变量。在建立了必要的定义之后，我证明了一个变形结果，该结果表明具有自然拓扑的空间$\Stab(\T)$是一个流形，可能是无限维的。
This paper introduces the notion of a stability condition on a triangulated category. The motivation comes from the study of Dirichlet branes in string theory, and especially from M.R. Douglas's notion of $\Pi$-stability. From a mathematical point of view, the most interesting feature of the definition is that the set of stability conditions $\Stab(\T)$ on a fixed category $\T$ has a natural topology, thus defining a new invariant of triangulated categories. After setting up the necessary definitions I prove a deformation result which shows that the space $\Stab(\T)$ with its natural topology is a manifold, possibly infinite-dimensional.