论文标题
$ Z $ - 关键连接和Bridgeland稳定性条件
$Z$-critical connections and Bridgeland stability conditions
论文作者
论文摘要
我们将霍明矢量束的几何偏微分方程与布里奇兰稳定性条件相关联。我们将这些方程式的解决方案称为$ z $ - 临界连接，中央费用为$ z $。变形的Hermitian Yang-Mills连接是一种特殊情况。我们解释了我们的方程式如何通过无限的维矩图自然出现。 我们的主要结果表明，在较大的体积限制中，一个足够光滑的全体形态矢量捆绑包在且仅当它渐近$ z $ stable时承认$ z $ - 批判性的连接。即使对于变形的Hermitian Yang-Mills方程，这也提供了更高排名的解决方案的第一个例子。
We associate geometric partial differential equations on holomorphic vector bundles to Bridgeland stability conditions. We call solutions to these equations $Z$-critical connections, with $Z$ a central charge. Deformed Hermitian Yang--Mills connections are a special case. We explain how our equations arise naturally through infinite dimensional moment maps. Our main result shows that in the large volume limit, a sufficiently smooth holomorphic vector bundle admits a $Z$-critical connection if and only if it is asymptotically $Z$-stable. Even for the deformed Hermitian Yang--Mills equation, this provides the first examples of solutions in higher rank.
