论文标题
最佳的符号连接和全体形态浸入的变形
Optimal Symplectic Connections and Deformations of Holomorphic Submersions
论文作者
论文摘要
我们对某些全态浸入的总空间进行了极端Kaehler指标的一般结构，从而扩展了Dervan-Sektnan，Fine和Hong的结果。我们认为，浸入纤维的浸入与纤维化稳定曲率的变性为kaehler歧管，与纤维结构兼容的方式。因此，我们允许k ksemession的纤维，而不是k-polystable；这对于模量理论至关重要。在这些纤维上，我们用一个部分微分方程表示，该方程称为最佳象征连接，代表了相对Kaehler度量的规范选择。我们希望这将是规范相对较高的kaehler公制的最通用的结构，只要所有输入都是平滑的。在绝热类别中，我们使用最佳符号连接的概念和与之相关的几何形状来构建具有恒定标量曲率和极端指标的Kaehler指标。
We give a general construction of extremal Kaehler metrics on the total space of certain holomorphic submersions, extending results of Dervan-Sektnan, Fine, and Hong. We consider submersions whose fibres admit a degeneration to Kaehler manifolds with constant scalar curvature, in a way that is compatible with the fibration structure. Thus we allow fibres that are K-semistable, rather than K-polystable; this is crucial to moduli theory. On these fibrations we phrase a partial differential equation whose solutions, called optimal symplectic connections, represent a canonical choice of a relatively Kaehler metric. We expect this to be the most general construction of a canonical relatively Kaehler metric provided all input is smooth. We use the notion of an optimal symplectic connection and the geometry related to it to construct Kaehler metrics with constant scalar curvature and extremal metrics on the total space, in adiabatic classes.
