发表机构
Università di Genova（热那亚大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在广义Grassmannian中完整分类了Picard秩1指数1的Fano四重簇，扩展了Küchle的结果，发现了三个新族，并计算了体积和Hodge数等不变量。
AI 中文摘要
我们给出了在广义Grassmannian（即Dynkin类型不同于A的Grassmannian）中，作为完全可约齐次向量丛的零轨迹得到的Picard秩为1且指数为1的Fano四重簇的完整分类。这扩展了Küchle在标准Grassmannian中完成的分类。在此过程中，我们展示了三个新的Picard秩为1且指数为1的Fano四重簇族。对于所研究的每个Fano四重簇，我们计算了若干数值不变量，如体积和Hodge数。
英文摘要
We provide a complete classification of Fano fourfolds of Picard rank 1 and index 1 obtained as zero loci of completely reducible homogeneous vector bundles in generalized Grassmannians, i.e. Grassmannians of Dynkin type different from A. This extends the classification done by Küchle in standard Grassmannians. In doing so, we exhibit three new families of Fano fourfolds of Picard rank 1 and index 1. For each of the studied Fano fourfolds, we compute several numerical invariants, such as volume and Hodge numbers.
