论文标题
负Kähler-Einstein表面的退化
Degenerations of Negative Kähler-Einstein Surfaces
论文作者
论文摘要
每个紧凑型Kähler歧管带有负面的Chern Class都承认一个唯一的度量$ G $，因此$ \ text {ric}（g）= -g $。了解这些指标的家庭如何退化，可以深入了解其几何形状，对于理解负Kähler-Einstein指标的模量空间的压缩至关重要。我研究了一个特殊的阶级，其中包括二等阶层。在Sun and Zhang（2019）在Calabi-Yau案例中的工作之后，我在中央纤维组件上构建了一个Kähler-Einstein颈部区域，在规范指标之间进行了插值。这为家庭中指标的限制几何形状提供了模型。
Every compact Kähler manifold with negative first Chern class admits a unique metric $g$ such that $\text{Ric}(g) = -g$. Understanding how families of these metrics degenerate gives insight into their geometry and is important for understanding the compactification of the moduli space of negative Kähler-Einstein metrics. I study a special class of such families in complex dimension two. Following the work of Sun and Zhang (2019) in the Calabi-Yau case, I construct a Kähler-Einstein neck region interpolating between canonical metrics on components of the central fiber. This provides a model for the limiting geometry of metrics in the family.
