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Abstract We classify the symplectic automorphism groups for cubic fourfolds. The main inputs are the global Torelli theorem for cubic fourfolds and the classification of the fixed-point sublattices of the Leech lattice. Among the highlights of our results, we note that there are 34 possible groups of symplectic automorphisms, with 6 maximal cases. The six maximal cases correspond to 8 non-isomorphic, and isolated in moduli, cubic fourfolds; six of them previously identified by other authors. Finally, the Fermat cubic fourfold has the largest possible order (174, 960) for the automorphism group (non-necessarily symplectic) among all smooth cubic fourfolds.
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This content will become publicly available on April 1, 2026
Classification of symplectic birational involutions of manifolds of OG10 type
Abstract We give a complete classification of symplectic birational involutions of manifolds ofOG10 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.
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- Award ID(s):
- 2101640
- PAR ID:
- 10579597
- Publisher / Repository:
- Springer Science
- Date Published:
- Journal Name:
- Mathematische Zeitschrift
- Volume:
- 309
- Issue:
- 4
- ISSN:
- 0025-5874
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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