Abstract:
In this paper we study locally transitive actions of the commutative unipotent group $\mathbb G_a^n$ on
a nondegenerate quadric in the projective space $\mathbb P^{n+1}$. It is shown that for each $n$ such an action is unique up to isomorphism.
Bibliography: 9 titles.
Keywords:
automorphisms of quadrics, locally transitive actions.
\Bibitem{Sha09}
\by E.~V.~Sharoiko
\paper Hassett-Tschinkel correspondence and automorphisms of the quadric
\jour Sb. Math.
\yr 2009
\vol 200
\issue 11
\pages 1715--1729
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This publication is cited in the following 17 articles:
Ivan Arzhantsev, “On conjugacy of additive actions in the affine Cremona group”, Quaestiones Mathematicae, 2024, 1
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Yingqi Liu, “Additive actions on hyperquadrics of corank two”, era, 30:1 (2022), 1
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Viktoriia Borovik, Sergey Gaifullin, Anton Trushin, “Commutative actions on smooth projective quadrics”, Communications in Algebra, 50:12 (2022), 5468
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R. A. Devyatov, “Commutative unipotent group actions on flag varieties and nilpotent multiplications”, Russian Math. Surveys, 69:5 (2014), 927–929
Ivan Arzhantsev, Andrey Popovskiy, Springer Proceedings in Mathematics & Statistics, 79, Automorphisms in Birational and Affine Geometry, 2014, 17
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