论文标题
沿着相交复杂线的圆锥形奇异性的卡拉比野指标：不稳定的情况
Calabi-Yau metrics with cone singularities along intersecting complex lines: the unstable case
论文作者
论文摘要
我们在$ \ Mathbf C^2 $上生产本地的Calabi-yau指标，并通过三个或更多复杂的线条，其锥形角度严格违反了Troyanov条件。原点处的切线锥是沿两个相交线的圆锥形奇异性的平坦的多面体kähler锥体：一个具有最小锥角的圆锥角对应的圆锥角，而另一个形式作为其余线的碰撞到单个圆锥线中。使用分支的覆盖参数，我们可以构建具有圆锥形曲线的Calabi-yau指标，并在不稳定范围内具有锥形角度。
We produce local Calabi-Yau metrics on $\mathbf C^2$ with conical singularities along three or more complex lines through the origin whose cone angles strictly violate the Troyanov condition. The tangent cone at the origin is a flat polyhedral Kähler cone with conical singularities along two intersecting lines: one with cone angle corresponding to the line with smallest cone angle, while the other forms as the collision of the remaining lines into a single conical line. Using a branched covering argument, we can construct Calabi-Yau metrics with cone singularities along cuspidal curves with cone angle in the unstable range.
