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.

我们研究渐近圆锥 Ricci-flat Kähler 度量的退化，因为 Kähler 类退化为半正类。我们表明，在适当的假设下，Ricci-flat Kähler 度量收敛到一个不完全平滑的 Ricci-flat Kähler 度量，远离紧凑的子变量。因此，我们在某些准射影变体上构造了具有无穷远渐近圆锥行为的奇异 Calabi-Yau 度量，并且我们证明了这些奇异度量的度量几何与奇异变体的拓扑同胚。最后，我们将应用我们的结果来研究 Calabi-Yau 流形之间几何过渡的几类例子。