The automorphism group of a rigid affine variety

被引：18

作者：

Arzhantsev, Ivan ^{[1
]}

Gaifullin, Sergey ^{[2
]}

机构：

[1] Natl Res Univ, Fac Comp Sci, Higher Sch Econ, Kochnovskiy Proezd 3, Moscow 125319, Russia

[2] Lomonosov Moscow State Univ, Fac Mech & Math, Dept Higher Algebra, Leninskie Gory 1, Moscow 119991, Russia

来源：

MATHEMATISCHE NACHRICHTEN | 2017年 / 290卷 / 5-6期

基金：

俄罗斯科学基金会;

关键词：

Affine variety; automorphism; graded algebra; torus action; trinomial; TORUS ACTION; MAKAR-LIMANOV; RINGS; SURFACES; CONES;

D O I：

10.1002/mana.201600295

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

An irreducible algebraic variety X is rigid if it admits no nontrivial action of the additive group of the ground field. We prove that the automorphism group Aut(X) of a rigid affine variety contains a unique maximal torus T. If the grading on the algebra of regular functions K[X] defined by the action of T is pointed, the group Aut( X) is a finite extension of T. As an application, we describe the automorphism group of a rigid trinomial affine hypersurface and find all isomorphisms between such hypersurfaces. (C) 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

引用

页码：662 / 671

页数：10

共 24 条

[1] Arzhantsev I., 2015, CAMBRIDGE STUDIES AD, V144
[2] Flag varieties, toric varieties, and suspensions: Three instances of infinite transitivity
Arzhantsev, I. V.
Zaidenberg, M. G.
Kuyumzhiyan, K. G.
[J]. SBORNIK MATHEMATICS, 2012, 203 (07) : 923 - 949
[3] On rigidity of factorial trinomial hypersurfaces
Arzhantsev, Ivan
[J]. INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 2016, 26 (05) : 1061 - 1070
[4] Arzhantsev I, 2014, MOSC MATH J, V14, P429
[5] On C-fibrations over Projective Curves
Bandman, Tatiana
Makar-Limanov, Leonid
[J]. MICHIGAN MATHEMATICAL JOURNAL, 2008, 56 (03) : 669 - 686
[6] Affine cones over smooth cubic surfaces
Cheltsov, Ivan
Park, Jihun
Won, Joonyeong
[J]. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2016, 18 (07) : 1537 - 1564
[7] Cox D. A., 1995, J ALGEBRAIC GEOM, V4, P17
[8] On the rigidity of small domains
Crachiola, A
Makar-Limanov, L
[J]. JOURNAL OF ALGEBRA, 2005, 284 (01) : 1 - 12
[9] Rigid Rings and Makar-Limanov Techniques
Crachiola, Anthony J.
Maubach, Stefan
[J]. COMMUNICATIONS IN ALGEBRA, 2013, 41 (11) : 4248 - 4266
[10] Dolgachev I, 2012, CLASS ALG GEOM MOD

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