Homogeneous locally nilpotent derivations of nonfactorial trinomial algebras. (English. Russian original) Zbl 1444.13034
Math. Notes 105, No. 6, 818-830 (2019); translation from Mat. Zametki 105, No. 6, 824-838 (2019).
Summary: 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.
References:
| [1] | G. Freudenburg, Algebraic Theory of Locally Nilpotent Derivations, in Encyclopaedia Math. Sci. (Springer, Berlin, 2006), Vol. 136. · Zbl 1121.13002 |
| [2] | I. Arzhantsev, J. Hausen, E. Herppich, and A. Liendo, “The automorphism group of a variety with torus action of complexity one,” Mosc. Math. J. 14 (3), 429-471 (2014). · Zbl 1332.14049 · doi:10.17323/1609-4514-2014-14-3-429-471 |
| [3] | I. Arzhantsev and S. Gaifullin, “The automorphism group of a rigid affine variety,” Math. Nachr. 290 (5-6), 662-671 (2017). · Zbl 1386.14156 · doi:10.1002/mana.201600295 |
| [4] | M. Demazure, “Sous-groupes algébriques de rang maximum du groupe de Cremona,” Ann. Sci. École Norm. Sup. (4) 3, 507-588 (1970). · Zbl 0223.14009 · doi:10.24033/asens.1201 |
| [5] | T. Oda, Convex Bodies and Algebraic Geometry. An Introduction to the Theory of Toric Varieties (Springer-Verlag, Berlin, 1988). · Zbl 0628.52002 |
| [6] | A. Liendo, “Affine <InlineEquation ID=”IEq2“> <EquationSource Format=”TEX“>\[ \mathbb{T} \] <EquationSource Format=”MATHML“> <math xmlns:xlink=”http://www.w3.org/1999/xlink“ display=”block“> <mi mathvariant=”double-struck“>T-varieties of complexity one and locally nilpotent derivations,”Transform. Groups 15 (2), 398-425 (2010). · Zbl 1209.14050 · doi:10.1007/s00031-010-9089-2 |
| [7] | I. Arzhantsev and A. Liendo, “Polyhedral divisors and SL2-actions on affine <InlineEquation ID=”IEq4“> <EquationSource Format=”TEX“>\[ \mathbb{T} \] <EquationSource Format=”MATHML“> <math xmlns:xlink=”http://www.w3.org/1999/xlink“ display=”block“> <mi mathvariant=”double-struck“>T-varieties,” Michigan Math. J. 61 (4), 731-762 (2012). · Zbl 1271.14090 · doi:10.1307/mmj/1353098511 |
| [8] | A. Liendo, “<InlineEquation ID=”IEq7“> <EquationSource Format=”TEX“>\[ \mathbb{G} \] <EquationSource Format=”MATHML“> <math xmlns:xlink=”http://www.w3.org/1999/xlink“ display=”block“> <mi mathvariant=”double-struck“>Ga-actions of fiber type on affine <InlineEquation ID=”IEq8“> <EquationSource Format=”TEX“>\[ \mathbb{T} \] <EquationSource Format=”MATHML“> <math xmlns:xlink=”http://www.w3.org/1999/xlink“ display=”block“> <mi mathvariant=”double-struck“>T-varieties,” J. Algebra 324 (12), 3653-3665 (2010). · Zbl 1219.14069 · doi:10.1016/j.jalgebra.2010.09.008 |
| [9] | B. Sturmfels, Gröbner Bases and Convex Polytopes, in Univ. Lecture Ser. (Amer. Math. Soc., Providence, RI, 1996), Vol. 8. · Zbl 0856.13020 |
| [10] | J. Hausen and H. Süß, “The Cox ring of an algebraic variety with torus action,” Adv. Math. 225 (2), 977-1012 (2010). · Zbl 1248.14008 · doi:10.1016/j.aim.2010.03.010 |
| [11] | J. Hausen, E. Herppich and H. Süß, “Multigraded factorial rings and Fano varieties with torus action,” Doc. Math. 16, 71-109 (2011). · Zbl 1222.13001 |
| [12] | Hausen, J.; Herppich, E., Factorially graded rings of complexity one, 414-428 (2013), Cambridge · Zbl 1290.13001 · doi:10.1017/CBO9781139525350.011 |
| [13] | J. Hausen and M. Wrobel, “Non-complete rational <Emphasis Type=”Italic“>T-varieties of complexity one,” Math. Nachr. 290 (5-6), 815-826 (2017). · Zbl 1371.13002 · doi:10.1002/mana.201600009 |
| [14] | I. Arzhantsev, “On rigidity of factorial trinomial hypersurfaces,” Internat. J. Algebra Comput. 26 (5), 1061-1070 (2016). · Zbl 1350.13008 · doi:10.1142/S0218196716500442 |
| [15] | S. Gaifullin, Automorphisms of Danielewski Varieties, arXiv: 1709.09237 (2017). · Zbl 1467.14153 |
| [16] | P. Yu. Kotenkova, Torus actions and locally nilpotent derivations, Cand. Sci. (Phys.-Math.) Dissertation (Moskov. Univ., Moscow, 2014) [in Russian]. |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
