标题： 卡拉比-丘对的复杂度为二的标准模型 显示英文标题

标题： Standard models for Calabi-Yau pairs of complexity two

摘要： 一个指标为一且复杂性为零的卡拉比-丘对是扇形的。 此外，一个指标为一且复杂性为一的卡拉比-丘对属于簇类型。 在本文中，我们研究指标为一且复杂性为二的卡拉比-丘对。 对于每个这样的对，我们或者证明其变更复杂性为零，或者将其与一个在扇形品种上的德尔珀诺纤维化相关联。 在后一种情况下，我们证明初始对属于簇类型当且仅当德尔珀诺纤维化属于簇类型。 我们给出了关于在扇形基上德尔珀诺纤维化属于簇类型的判别准则。 在此过程中，我们证明了一个关于在扇形基上卡拉比-丘对族中的共正则性不变性的陈述。 显示英文摘要

摘要： A Calabi-Yau pair of index one and complexity zero is toric. Furthermore, a Calabi-Yau pair of index one and complexity one is of cluster type. In this article, we study Calabi-Yau pairs of index one and complexity two. For each such pair, we either prove that its alteration complexity is zero or we associate to it a del Pezzo fibration over a toric variety. In the latter case, we show that the initial pair is of cluster type if and only if the del Pezzo fibration is of cluster type. We give criteria for del Pezzo fibrations over toric bases to be of cluster type. Along the way, we prove a statement about the invariance of the coregularity in families of Calabi-Yau pairs over toric bases.