Abstract
In the article strongly nondegenerate (k, n)-quadrics all of whose linear automorphisms are of the formz→μz, ω → ¦μ¦2ω, μ ∈ ℂ {0} are considered. Quadrics all of whose linear automorphisms are of this form were calledc-rigid by V. Beloshapka. The main result of the article is the following: anyc-rigid strongly nondegenerate (k, n)-quadric has no nonlinear automorphisms. A table indicating the relationship between linear and nonlinear automorphisms for (k, n)-quadrics is presented.
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References
N. Palinchak, “About quadrics of high codimensions,”Mat. Zametki [Math. Notes],55, No. 5, 110–115 (1994).
V. Beloshapka, “About holomorphic transformations of quadrics,”Mat. Sb. [Math. USSR-Sb.],182, No. 2, 203–219 (1991).
V. Beloshapka, “Uniqueness theorem for automorphisms of nondegenerate surface in complex space,”Mat. Zametki [Math. Notes],47, No. 3, 17–22 (1990)
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Translated fromMatematicheskie Zametki, Vol. 59, No. 2, pp. 224–229, February, 1996.
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Palinchak, N. About C-rigid quadrics. Math Notes 59, 158–162 (1996). https://doi.org/10.1007/BF02310955
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DOI: https://doi.org/10.1007/BF02310955