scholarly journals Global rigidity of solvable group actions onS1

2004 ◽  
Vol 8 (2) ◽  
pp. 877-924 ◽  
Author(s):  
Lizzie Burslem ◽  
Amie Wilkinson
Keyword(s):  
Solvable Group ◽  
Group Actions ◽  
Global Rigidity

scholarly journals Topological transitivity of solvable group actions on the line R

2009 ◽  
Vol 116 (2) ◽  
pp. 203-215 ◽  
Author(s):  
Suhua Wang ◽  
Enhui Shi ◽  
Lizhen Zhou ◽  
Grant Cairns
Keyword(s):  
Solvable Group ◽  
Group Actions ◽  
Topological Transitivity

scholarly journals Measure rigidity for solvable group actions in the space of lattices

2019 ◽  
Vol 189 (3) ◽  
pp. 421-428
Author(s):  
Manfred Einsiedler ◽  
Ronggang Shi
Keyword(s):  
Solvable Group ◽  
Group Actions ◽  
Measure Rigidity

scholarly journals Global rigidity of some abelian-by-cyclic group actions on 𝕋2

2021 ◽  
Vol 25 (6) ◽  
pp. 3133-3178
Author(s):  
Sebastian Hurtado ◽  
Jinxin Xue
Keyword(s):  
Cyclic Group ◽  
Group Actions ◽  
Global Rigidity

Group actions and non-vanishing elements in solvable groups

2020 ◽  
Vol 23 (6) ◽  
pp. 1103-1109
Author(s):  
Thomas R. Wolf
Keyword(s):  
Solvable Group ◽  
Group Actions ◽  
Solvable Groups ◽  
Direct Sum ◽  
Irreducible Modules ◽  
Group A ◽  
Vanishing Elements

AbstractFor a solvable group, a theorem of Gaschutz shows that {F(G)/\Phi(G)} is a direct sum of irreducible G-modules and a faithful {G/F(G)}-module. If each of these irreducible modules is primitive, we show that every non-vanishing element of G lies in {F(G)}.

Generating pairs and group actions

2014 ◽  
Vol 218 (5) ◽  
pp. 777-783
Author(s):  
Darryl McCullough
Keyword(s):  
Group Actions

scholarly journals The close relation between border and Pommaret marked bases

2021 ◽  
Author(s):  
Cristina Bertone ◽  
Francesca Cioffi
Keyword(s):  
Finite Order ◽  
Polynomial Ring ◽  
Group Actions ◽  
Close Relation ◽  
Open Covering ◽  
Order Ideal ◽  
Lower Dimension ◽  
Hilbert Schemes ◽  
Affine Spaces ◽  
The Ideal

AbstractGiven a finite order ideal $${\mathcal {O}}$$ O in the polynomial ring $$K[x_1,\ldots , x_n]$$ K [ x 1 , … , x n ] over a field K, let $$\partial {\mathcal {O}}$$ ∂ O be the border of $${\mathcal {O}}$$ O and $${\mathcal {P}}_{\mathcal {O}}$$ P O the Pommaret basis of the ideal generated by the terms outside $${\mathcal {O}}$$ O . In the framework of reduction structures introduced by Ceria, Mora, Roggero in 2019, we investigate relations among $$\partial {\mathcal {O}}$$ ∂ O -marked sets (resp. bases) and $${\mathcal {P}}_{\mathcal {O}}$$ P O -marked sets (resp. bases). We prove that a $$\partial {\mathcal {O}}$$ ∂ O -marked set B is a marked basis if and only if the $${\mathcal {P}}_{\mathcal {O}}$$ P O -marked set P contained in B is a marked basis and generates the same ideal as B. Using a functorial description of these marked bases, as a byproduct we obtain that the affine schemes respectively parameterizing $$\partial {\mathcal {O}}$$ ∂ O -marked bases and $${\mathcal {P}}_{\mathcal {O}}$$ P O -marked bases are isomorphic. We are able to describe this isomorphism as a projection that can be explicitly constructed without the use of Gröbner elimination techniques. In particular, we obtain a straightforward embedding of border schemes in affine spaces of lower dimension. Furthermore, we observe that Pommaret marked schemes give an open covering of Hilbert schemes parameterizing 0-dimensional schemes without any group actions. Several examples are given throughout the paper.

scholarly journals Schottky groups acting on homogeneous rational manifolds

2019 ◽  
Vol 2019 (753) ◽  
pp. 23-56 ◽  
Author(s):  
Christian Miebach ◽  
Karl Oeljeklaus
Keyword(s):  
Deformation Theory ◽  
Group Actions ◽  
Picard Group ◽  
Schottky Group ◽  
Fundamental Groups ◽  
Complex Manifolds ◽  
Schottky Groups ◽  
Algebraic Dimension ◽  
Geometric Invariants ◽  
Compact Complex Manifolds

AbstractWe systematically study Schottky group actions on homogeneous rational manifolds and find two new families besides those given by Nori’s well-known construction. This yields new examples of non-Kähler compact complex manifolds having free fundamental groups. We then investigate their analytic and geometric invariants such as the Kodaira and algebraic dimension, the Picard group and the deformation theory, thus extending results due to Lárusson and to Seade and Verjovsky. As a byproduct, we see that the Schottky construction allows to recover examples of equivariant compactifications of {{\rm{SL}}(2,\mathbb{C})/\Gamma} for Γ a discrete free loxodromic subgroup of {{\rm{SL}}(2,\mathbb{C})}, previously obtained by A. Guillot.

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