Unipotent group actions on projective varieties

2019 ◽  
Author(s):  
Rajendra V. Gurjar ◽  
Kayo Masuda ◽  
Masayoshi Miyanishi
Keyword(s):  
Group Actions ◽  
Unipotent Group ◽  
Projective Varieties

Geometric Quotients of Unipotent Group Actions

1993 ◽  
Vol s3-67 (1) ◽  
pp. 75-105 ◽  
Author(s):  
Gert-Martin Greuel ◽  
Gerhard Pfister
Keyword(s):  
Group Actions ◽  
Unipotent Group

scholarly journals Geometric Quotients of Unipotent Group Actions II

Singularities ◽  
1998 ◽  
pp. 27-36 ◽  
Author(s):  
Gert-Martin Greuel ◽  
Gerhard Pfister
Keyword(s):  
Group Actions ◽  
Unipotent Group

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 Unipotent group actions on del Pezzo cones

2014 ◽  
pp. 46-56 ◽  
Author(s):  
Takashi Kishimoto ◽  
Yuri Prokhorov ◽  
Mikhail Zaidenberg
Keyword(s):  
Group Actions ◽  
Unipotent Group ◽  
Del Pezzo

scholarly journals Unipotent group actions: corrections

1988 ◽  
Vol 50 (2) ◽  
pp. 209-210 ◽  
Author(s):  
Amassa Fauntleroy
Keyword(s):  
Group Actions ◽  
Unipotent Group

scholarly journals Free abelian group actions on normal projective varieties: submaximal dynamical rank case

2020 ◽  
pp. 1-17
Author(s):  
Fei Hu ◽  
Sichen Li
Keyword(s):  
Abelian Group ◽  
Projective Variety ◽  
Free Abelian Group ◽  
Group Actions ◽  
Maximal Rank ◽  
Positive Entropy ◽  
Projective Varieties ◽  
Group Of Automorphisms ◽  
Abelian Group Actions ◽  
De Qi

Abstract Let X be a normal projective variety of dimension n and G an abelian group of automorphisms such that all elements of $G\setminus \{\operatorname {id}\}$ are of positive entropy. Dinh and Sibony showed that G is actually free abelian of rank $\le n - 1$ . The maximal rank case has been well understood by De-Qi Zhang. We aim to characterize the pair $(X, G)$ such that $\operatorname {rank} G = n - 2$ .

scholarly journals Hamiltonian actions of unipotent groups on compact K\"ahler manifolds

2018 ◽  
Vol Volume 2 ◽  
Author(s):  
Daniel Greb ◽  
Christian Miebach
Keyword(s):  
Lie Groups ◽  
Invariant Theory ◽  
Symplectic Reduction ◽  
Stability Conditions ◽  
Unipotent Group ◽  
Geometric Invariant ◽  
Projective Varieties ◽  
Final Version ◽  
Unipotent Groups ◽  
Hamiltonian Actions

We study meromorphic actions of unipotent complex Lie groups on compact K\"ahler manifolds using moment map techniques. We introduce natural stability conditions and show that sets of semistable points are Zariski-open and admit geometric quotients that carry compactifiable K\"ahler structures obtained by symplectic reduction. The relation of our complex-analytic theory to the work of Doran--Kirwan regarding the Geometric Invariant Theory of unipotent group actions on projective varieties is discussed in detail. Comment: v2: 30 pages, final version as accepted by EPIGA

scholarly journals Unipotent group actions on affine varieties

2011 ◽  
Vol 336 (1) ◽  
pp. 200-208 ◽  
Author(s):  
H. Derksen ◽  
A. van den Essen ◽  
D.R. Finston ◽  
S. Maubach
Keyword(s):  
Group Actions ◽  
Unipotent Group
Sign in / Sign up

Export Citation Format

Share Document