8
Views
0
CrossRef citations to date
0
Altmetric
Online First Articles

On conjugacy of additive actions in the affine Cremona group

Received 12 Jan 2024, Published online: 15 May 2024

References

  • Ivan Arzhantsev, Sergey Bragin, and Yulia Zaitseva, Commutative algebraic monoid structures on affine spaces, Commun. Contemp. Math. 22(8) (2020), article 1950064. doi: 10.1142/S0219199719500640
  • Ivan Arzhantsev and Andrey Popovskiy, Additive actions on projective hypersurfaces, In: Automorphisms in Birational and Affine Geometry, Springer Proc. Math. Stat., Vol. 79, pp. 17–33, Springer, Cham/Heidelberg/New York/Dordrecht/London, 2014.
  • Ivan Arzhantsev and Elena Romaskevich, Additive actions on toric varieties, Proc. Amer. Math. Soc. 145(5) (2017), 1865–1879. doi: 10.1090/proc/13349
  • Ivan Arzhantsev and Yulia Zaitseva, Equivariant completions of affine spaces, Russian Math. Surveys 77(4) (2022), 571–650. doi: 10.4213/rm10046e
  • Ivan Beldiev, Gorenstein algebras and uniqueness of additive actions, Results Math. 78(5) (2023), article 192. doi: 10.1007/s00025-023-01972-w
  • Florian Berchtold, Lifting of morphisms to quotient presentations, Manuscripta Math. 110(1) (2003), 33–44. doi: 10.1007/s00229-002-0297-5
  • Jérémy Blanc, Conjugacy classes of affine automorphisms of and linear automorphisms of in the Cremona groups, Manuscripta Math. 119(2) (2006), 225–241. doi: 10.1007/s00229-005-0617-7
  • Michel Brion, On models of algebraic group actions, Proc. Indian Acad. Sci. (Math. Sci.) 132 (2022), article 61.
  • Michel Demazure, Sous-groupes algébriques de rang maximum du groupe de Cremona, Ann. Sci. Éc. Norm. Supér. 3 (1970), 507–588. doi: 10.24033/asens.1201
  • Rostislav Devyatov, Unipotent commutative group actions on flag varieties and nilpotent multiplications, Transform. Groups 20(1) (2015), 21–64. doi: 10.1007/s00031-015-9306-0
  • Adrien Dubouloz, Takashi Kishimoto, and Pedro Montero, Del Pezzo quintics as equivariant compactifications of vector groups, arXiv:2209.04152.
  • Sergey Dzhunusov, Additive actions on complete toric surfaces, Internat. J. Algebra Comput. 31(1) (2021), 19–35. doi: 10.1142/S0218196721500028
  • Sergey Dzhunusov, On uniqueness of additive actions on complete toric varieties, J. Algebra 609 (2022), 642–656. doi: 10.1016/j.jalgebra.2022.06.016
  • Baohua Fu and Jun-Muk Hwang, Uniqueness of equivariant compactifications of by a Fano manifold of Picard number 1, Math. Res. Lett. 21(1) (2014), 121–125. doi: 10.4310/MRL.2014.v21.n1.a9
  • Brendan Hassett and Yuri Tschinkel, Geometry of equivariant compactifications of , Int. Math. Res. Not. IMRN 1999(22) (1999), 1211–1230. doi: 10.1155/S1073792899000665
  • Friedrich Knop and Herbert Lange, Commutative algebraic groups and inter-sections of quadrics, Math. Ann. 267(4) (1984), 555–571. doi: 10.1007/BF01455973
  • Yingqi Liu, Additive actions on hyperquadrics of corank two, Electron. Res. Arch. 30(1) (2022), 1–34. doi: 10.3934/era.2022001
  • Guerino Mazzola, Generic finite schemes and Hochschild cocycles, Comment. Math. Helv. 55 (1980), 267–293. doi: 10.1007/BF02566686
  • Bjorn Poonen, Isomorphism types of commutative algebras of finite rank over an algebraically closed field, Computational Arithmetic Geometry, 111-120, Contemp. Math. 463, Amer. Math. Soc., Providence, RI, 2008.
  • Anton Shafarevich, Additive actions on toric projective hypersurfaces, Results Math. 76(3) (2021), art. 145. doi: 10.1007/s00025-021-01462-x
  • Elena Sharoiko, Hassett-Tschinkel correspondence and automorphisms of a quadric, Sb. Math. 200(11) (2009), 1715–1729. doi: 10.1070/SM2009v200n11ABEH004056
  • Dmitri Suprunenko and Regina Tyshkevich, Commutative Matrices, Academic Press, New York, 1968.
  • André Weil, On algebraic groups of transformations, Amer. J. Math. 77 (1955), 355–391. doi: 10.2307/2372535
  • Dmitri Zaitsev, Regularization of birational group operations in the sense of Weil, J. Lie Theory 5(2) (1995), 207–224.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.