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Tsinghua University（清华大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文利用格论和OSCAR枚举算法，完成了42族光滑四次三维簇的所有可能自同构群分类，基于周期映射已知结果。
AI 中文摘要
Laza 与第二作者已分类了光滑四次三维簇的所有可能辛自同构群，共有 34 个这样的群。根据 Koike 的结果，具有指定辛自同构群的四次三维簇有 48 个族。对于其中 42 个族，我们完成了所有可能自同构群的分类。本文方法主要基于格论，从 Voisin、Hassett、Looijenga 和 Laza 关于四次三维簇周期映射的已知结果出发，并使用 OSCAR 中实现的格枚举算法。
英文摘要
Laza and the second author have classified all possible symplectic automorphism groups of smooth cubic fourfolds. There are $34$ such groups, and by Koike, there are $48$ families of cubic fourfolds with speficied symplectic automorphism group. For $42$ among those families, we complete the classification of all possible automorphism groups. The approach of this paper is mainly lattice theoretic, starting from known results about the period map of cubic fourfolds by Voisin, Hassett, Looijenga and Laza. We use a lattice-enumeration algorithm implemented in OSCAR.
Comments26 pages, comments welcome!
