Geodesic
Hassett-Tschinkel correspondence and automorphisms of the quadric
Sbornik. Mathematics, Tome 200 (2009) no. 11, pp. 1715-1729 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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E. V. Sharoiko. Hassett-Tschinkel correspondence and automorphisms of the quadric. Sbornik. Mathematics, Tome 200 (2009) no. 11, pp. 1715-1729. http://geodesic.mathdoc.fr/item/SM_2009_200_11_a5/

[1] B. Hassett, Yu. Tschinkel, “Geometry of equivariant compactifications of $\mathbb G^n_a$”, Internat. Math. Res. Notices, 22 (1999), 1211–1230 | DOI | MR | Zbl

[2] D. A. Suprunenko, R. I. Tyshkevich, Perestanovochnye matritsy, Nauka i tekhnika, Minsk, 1966 | MR | Zbl

[3] H. Matsumura, P. Monsky, “On the automorphisms of hypersurfaces”, J. Math. Kyoto Univ., 3 (1964), 347–361 | MR | Zbl

[4] M. Doebeli, “Reductive group actions on affine quadrics with 1-dimensional quotient: Linearization when a linear model exists”, Transform. Groups, 1:3 (1996), 187–214 | DOI | MR | Zbl

[5] B. Totaro, “The automorphism group of an affine quadric”, Math. Proc. Cambridge Philos. Soc., 143:1 (2007), 1–8 | DOI | MR | Zbl

[6] D. N. Akhiezer, “On the modality and complexity of actions of reductive groups”, Russian Math. Surveys, 43:2 (1988), 157–158 | DOI | MR | Zbl

[7] I. V. Arzhantsev, “On modality and complexity of affine embeddings”, Sb. Math., 192:8 (2001), 1133–1138 | DOI | MR | Zbl

[8] V. L. Popov, Eh. B. Vinberg, “Invariant theory”, Algebraic geometry. IV. Linear algebraic groups, invariant theory, Encyclopaedia Math. Sci., 55, Springer-Verlag, Berlin, 1994, 123–278 | MR | MR | Zbl | Zbl

[9] V. Hussin, P. Winternitz, H. Zassenhaus, “Maximal abelian subalgebras of complex orthogonal Lie algebras”, Linear Algebra Appl., 141 (1990), 183–220 | DOI | MR | Zbl