论文标题
关于全态纤维束的规范指标
Canonical metrics on holomorphic fibre bundles
论文作者
论文摘要
在本文中，我们彻底描述了各向同性的Kähler纤维上的规范指标，称为最佳符号连接。在这种设置中，相对自动形态的全体形态主束上的Hermite-einstein连接引起了最佳的符号连接，而Hitchin-kobayashi通信则确切地认为，当主束值得一键时，这种联系的存在。结合Dervan和Sektnan的结果，这为Holomorthic Fiber束的总空间生成了许多CSCK指标的新示例。我们的结果表明，通常，最佳的符号连接方程应视为HERMITE-Einstein方程对纤维纤维的复杂结构各不相同的Helmite-Einstein方程的概括。
In this article we completely describe the existence of canonical metrics, known as optimal symplectic connections, on isotrivial Kähler fibrations. In this setting an optimal symplectic connection is induced from a Hermite--Einstein connection on the holomorphic principal bundle of relative automorphisms, and the Hitchin--Kobayashi correspondence asserts the existence of such a connection precisely when the principal bundle is polystable. Combined with results of Dervan and Sektnan this generates many new examples of cscK metrics on the total space of holomorphic fibre bundles. Our results indicate that in general the optimal symplectic connection equation should be viewed as a generalisation of the Hermite--Einstein equation to holomorphic fibrations where the complex structure of the fibres varies.
