Abstract
The forms of the Segre cubic over non-algebraically closed fields, their automorphisms groups, and equivariant birational rigidity are studied. In particular, it is shown that all forms of the Segre cubic over any field have a point and are cubic hypersurfaces.
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Acknowledgments
The author is a winner of the competition “Young Mathematics of Russia” and thanks its jury. The author expresses gratitude to S. Gorchinskii, A. Trepalin, and K. Shramov for valuable comments.
Funding
This work was supported by the Russian Science Foundation under grant 18-11-00121.
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Russian Text © The Author(s), 2020, published in Matematicheskie Zametki, 2020, Vol. 107, No. 1, pp. 3–10.
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Avilov, A.A. Forms of the Segre Cubic. Math Notes 107, 3–9 (2020). https://doi.org/10.1134/S0001434620010010
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DOI: https://doi.org/10.1134/S0001434620010010