Geodesic
Homogeneous Locally Nilpotent Derivations of Nonfactorial Trinomial Algebras
Matematičeskie zametki, Tome 105 (2019) no. 6, pp. 824-838.

Voir la notice de l'article provenant de la source Math-Net.Ru

We describe homogeneous locally nilpotent derivations of the algebra of regular functions for a class of affine trinomial hypersurfaces. This class comprises all nonfactorial trinomial hypersurfaces.
Mots-clés : affine hypersurface, torus action
Keywords: graded algebra, derivation. 
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Yu. I. Zaitseva. Homogeneous Locally Nilpotent Derivations of Nonfactorial Trinomial Algebras. Matematičeskie zametki, Tome 105 (2019) no. 6, pp. 824-838. http://geodesic.mathdoc.fr/item/MZM_2019_105_6_a2/

[1] G. Freudenburg, “Algebraic Theory of Locally Nilpotent Derivations”, Encyclopaedia Math. Sci., 136, Springer, Berlin, 2006 | MR | Zbl

[2] I. Arzhantsev, J. Hausen, E. Herppich, A. Liendo, “The automorphism group of a variety with torus action of complexity one”, Mosc. Math. J., 14:3 (2014), 429–471 | MR | Zbl

[3] I. Arzhantsev, S. Gaifullin, “The automorphism group of a rigid affine variety”, Math. Nachr., 290:5-6 (2017), 662–671 | DOI | MR | Zbl

[4] M. Demazure, “Sous-groupes algébriques de rang maximum du groupe de Cremona”, Ann. Sci. École Norm. Sup. (4), 3 (1970), 507–588 | DOI | MR | Zbl

[5] T. Oda, Convex Bodies and Algebraic Geometry. An Introduction to the Theory of Toric Varieties, Springer-Verlag, Berlin, 1988 | MR | Zbl

[6] A. Liendo, “Affine $\mathbb{T}$-varieties of complexity one and locally nilpotent derivations”, Transform. Groups, 15:2 (2010), 398–425 | MR

[7] I. Arzhantsev, A. Liendo, “Polyhedral divisors and $\text{SL}_2$-actions on affine $\mathbb T$-varieties”, Michigan Math. J., 61:4 (2012), 731–762 | DOI | MR | Zbl

[8] A. Liendo, “$\mathbb{G}_a$-actions of fiber type on affine $\mathbb{T}$-varieties”, J. Algebra, 324:12 (2010), 3653–3665 | DOI | MR | Zbl

[9] B. Sturmfels, “Gröbner Bases and Convex Polytopes”, Univ. Lecture Ser., 8, Amer. Math. Soc., Providence, RI, 1996 | MR | Zbl

[10] J. Hausen, H. Süß, “The Cox ring of an algebraic variety with torus action”, Adv. Math., 225:2 (2010), 977–1012 | DOI | MR | Zbl

[11] J. Hausen, E. Herppich, H. Süß, “Multigraded factorial rings and Fano varieties with torus action”, Doc. Math., 16 (2011), 71–109 | MR | Zbl

[12] J. Hausen, E. Herppich, “Factorially graded rings of complexity one”, Torsors, Étale Homotopy and Applications to Rational Points, London Math. Soc. Lecture Note Ser.,, 405, Cambridge Univ. Press, Cambridge, 2013, 414–428 | MR | Zbl

[13] J. Hausen, M. Wrobel, “Non-complete rational $T$-varieties of complexity one”, Math. Nachr., 290:5-6 (2017), 815–826 | DOI | MR | Zbl

[14] I. Arzhantsev, “On rigidity of factorial trinomial hypersurfaces”, Internat. J. Algebra Comput., 26:5 (2016), 1061–1070 | DOI | MR | Zbl

[15] S. Gaifullin, Automorphisms of Danielewski Varieties, 2017, arXiv: 1709.09237

[16] P. Yu. Kotenkova, Deistviya torov i lokalno nilpotentnye differentsirovaniya, Dis. $\dots$ kand. fiz.-matem. nauk, Mosk. un-t, M., 2014