We associate with a generalised deep hole of the Leech lattice vertex operator algebra a generalised hole diagram. We show that this Dynkin diagram determines the generalised deep hole up to conjugacy and that there are exactly $70$ such diagrams. In an earlier work we proved a bijection between the generalised deep holes and the strongly rational, holomorphic vertex operator algebras of central charge $24$ with nontrivial weight-$1$ space. Hence, we obtain a new, geometric classification of these vertex operator algebras, generalising the classification of the Niemeier lattices by their hole diagrams.

中文翻译：

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中心电荷全纯顶点算子代数的几何分类 24

我们将Leech点阵顶点算子代数的广义深孔与广义孔图联系起来。我们表明，这个 Dynkin 图确定了共轭的广义深孔，并且确切地存在 $70$ 这样的图表。在早期的工作中，我们证明了广义深洞与中心电荷的强有理全纯顶点算子代数之间的双射>具有非平凡的权重-1空间。因此，我们获得了这些顶点算子代数的新的几何分类，通过孔图概括了尼迈尔格的分类。