scholarly journals Jordan property for algebraic groups and automorphism groups of projective varieties in arbitrary characteristic

2020 ◽  
Vol 69 (7) ◽  
pp. 2493-2504
Author(s):  
Fei Hu
Keyword(s):  
Automorphism Groups ◽  
Algebraic Groups ◽  
Projective Varieties ◽  
Arbitrary Characteristic

scholarly journals Abelian Varieties as Automorphism Groups of Smooth Projective Varieties

2018 ◽  
Vol 2020 (7) ◽  
pp. 1942-1956
Author(s):  
Davide Lombardo ◽  
Andrea Maffei
Keyword(s):  
Automorphism Group ◽  
Projective Variety ◽  
Automorphism Groups ◽  
Abelian Varieties ◽  
Smooth Projective Variety ◽  
Projective Varieties ◽  
Smooth Projective Varieties

Abstract We determine which complex abelian varieties can be realized as the automorphism group of a smooth projective variety.

scholarly journals Computing invariants of algebraic groups in arbitrary characteristic

2008 ◽  
Vol 217 (5) ◽  
pp. 2089-2129 ◽  
Author(s):  
Harm Derksen ◽  
Gregor Kemper
Keyword(s):  
Algebraic Groups ◽  
Arbitrary Characteristic

EXTENSIONS OF ALGEBRAIC GROUPS THAT ARE TRANSITIVE ON PROJECTIVE VARIETIES

1980 ◽  
Vol 35 (2) ◽  
pp. 237-238
Author(s):  
M T El'baradi
Keyword(s):  
Algebraic Groups ◽  
Projective Varieties

Jordan property and automorphism groups of normal compact Kähler varieties

2018 ◽  
Vol 20 (03) ◽  
pp. 1750024 ◽  
Author(s):  
Jin Hong Kim
Keyword(s):  
Automorphism Group ◽  
Automorphism Groups ◽  
Projective Varieties ◽  
Full Automorphism Group ◽  
Identity Component ◽  
Arbitrary Dimensions ◽  
Type Decomposition

It has been recently shown by Meng and Zhang that the full automorphism group [Formula: see text] is a Jordan group for all projective varieties in arbitrary dimensions. The aim of this paper is to show that the full automorphism group [Formula: see text] is, in fact, a Jordan group even for all normal compact Kähler varieties in arbitrary dimensions. The meromorphic structure of the identity component of the automorphism group and its Rosenlicht-type decomposition play crucial roles in the proof.

scholarly journals Outer unipotent classes in automorphism groups of simple algebraic groups

2014 ◽  
Vol 109 (3) ◽  
pp. 553-595 ◽  
Author(s):  
Ross Lawther ◽  
Martin W. Liebeck ◽  
Gary M. Seitz
Keyword(s):  
Automorphism Groups ◽  
Algebraic Groups

scholarly journals Derived length of zero entropy groups acting on projective varieties in arbitrary characteristic — A remark to a paper of Dinh-Oguiso-Zhang

2020 ◽  
Vol 31 (08) ◽  
pp. 2050059
Author(s):  
Sichen Li
Keyword(s):  
Projective Variety ◽  
Type Theorem ◽  
Closed Field ◽  
Unipotent Group ◽  
Projective Varieties ◽  
Arbitrary Characteristic ◽  
Derived Length ◽  
Dimension Formula ◽  
Zero Entropy ◽  
Finite Index Subgroup

Let [Formula: see text] be a projective variety of dimension [Formula: see text] over an algebraically closed field of arbitrary characteristic. We prove a Fujiki–Lieberman type theorem on the structure of the automorphism group of [Formula: see text]. Let [Formula: see text] be a group of zero entropy automorphisms of [Formula: see text] and [Formula: see text] the set of elements in [Formula: see text] which are isotopic to the identity. We show that after replacing [Formula: see text] by a suitable finite-index subgroup, [Formula: see text] is a unipotent group of the derived length at most [Formula: see text]. This result was first proved by Dinh et al. for compact Kähler manifolds.

scholarly journals Jordan property for non-linear algebraic groups and projective varieties

2018 ◽  
Vol 140 (4) ◽  
pp. 1133-1145 ◽  
Author(s):  
Sheng Meng ◽  
De-Qi Zhang
Keyword(s):  
Algebraic Groups ◽  
Projective Varieties ◽  
Linear Algebraic Groups ◽  
Non Linear

scholarly journals Adjoint algebraic groups as automorphism groups of a projector on a central simple algebra

2020 ◽  
Vol 560 ◽  
pp. 574-578
Author(s):  
Viktor A. Petrov ◽  
Andrei V. Semenov
Keyword(s):  
Automorphism Groups ◽  
Algebraic Groups ◽  
Central Simple Algebra ◽  
Simple Algebra ◽  
Central Simple
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