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<p>We give a complete classification of symplectic birational involutions of manifolds of <i>OG</i>10 type. We approach this classification with three techniques—via involutions of the Leech lattice, via involutions of cubic fourfolds, and finally lattice enumeration via a modified Kneser’s neighbour algorithm. The classification consists of three involutions with an explicit geometric realisation via cubic fourfolds, and three exceptional involutions which cannot be obtained by any known construction.</p>

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Classification of symplectic birational involutions of manifolds of OG10 type

  • 期刊论文

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  • 发表日期：

    2025年2月25日

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  • Lisa Marquand,
  • Stevell Muller

摘要

We give a complete classification of symplectic birational involutions of manifolds of OG10 type. We approach this classification with three techniques—via involutions of the Leech lattice, via involutions of cubic fourfolds, and finally lattice enumeration via a modified Kneser’s neighbour algorithm. The classification consists of three involutions with an explicit geometric realisation via cubic fourfolds, and three exceptional involutions which cannot be obtained by any known construction.