论文标题
复曲面的Kähler几何形状
The Kähler geometry of toric manifolds
论文作者
论文摘要
这些讲义是为我在2019年在卢米尼（Cirm in Luminy）的Cirm in Luminy上提供的博士学位小道编写的。他们的预期目的是在光滑的感谢您的品种的背景下，这是一个相对具有独立的和基础的介绍，对极端Kähler量学理论的介绍是E. Calabi在1980年和广泛开发的。在符号和代数几何形状中使用的复曲面歧管的框架为极端Kähler指标的一般理论提供了肥沃的测试地面，并提供了一类重要的平滑复杂品种，现在以相应的Delzant Polytope的稳定性条件来理解存在理论。这些笔记不包含任何原始材料，也不考虑一些最新的发展，例如针对卡拉比问题的非一切本发展。我在Arxiv上提供它们，因为我继续对如何引用它们的疑问。
These lecture notes are written for a PhD mini-course I gave at the CIRM in Luminy in 2019. Their intended purpose was to present, in the context of smooth toric varieties, a relatively self-contained and elementary introduction to the theory of extremal Kähler metrics pioneered by E. Calabi in the 1980's and extensively developed in recent years. The framework of toric manifolds, used in both symplectic and algebraic geometry, offers a fertile testing ground for the general theory of extremal Kähler metrics and provides an important class of smooth complex varieties for which the existence theory is now understood in terms of a stability condition of the corresponding Delzant polytope. The notes do not contain any original material nor do they take into account some more recent developments, such as the non-Archimedean approach to the Calabi problem. I am making them available on the arXiv because I continue to get questions about how they can be cited.
