论文标题
关于渐近的圆锥形calabi-yau指标的变性
On the degeneration of asymptotically conical Calabi-Yau metrics
论文作者
论文摘要
我们研究了Kähler类退化为半阳性类别的Kähler类别，研究了渐近圆锥形的ricci-flatKähler指标的退化。我们表明，在适当的假设下，ricci-flatKähler指标会收敛到不完整的平滑ricci-flatKähler指标，从而远离紧凑型亚种。结果，我们在某些准标记品种上构建了奇异的calabi-yau指标，在无穷大的无限范围内具有渐近的圆锥形行为，并且我们表明这些奇异指标的度量几何形状对于奇异品种的拓扑是同件。最后，我们将应用结果研究卡拉比YAU歧管之间的几种几何跃迁示例。
We study the degenerations of asymptotically conical Ricci-flat Kähler metrics as the Kähler class degenerates to a semi-positive class. We show that under appropriate assumptions, the Ricci-flat Kähler metrics converge to a incomplete smooth Ricci-flat Kähler metric away from a compact subvariety. As a consequence, we construct singular Calabi-Yau metrics with asymptotically conical behaviour at infinity on certain quasi-projective varieties and we show that the metric geometry of these singular metrics are homeomorphic to the topology of the singular variety. Finally, we will apply our results to study several classes of examples of geometric transitions between Calabi-Yau manifolds.
