scholarly journals Bestvina complex for group actions with a strict fundamental domain

2020 ◽  
Vol 14 (4) ◽  
pp. 1277-1307
Author(s):  
Nansen Petrosyan ◽  
Tomasz Prytuła
Keyword(s):  
Fundamental Domain ◽  
Group Actions

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.

scholarly journals Lifting group actions and nonnegative curvature

2011 ◽  
Vol 363 (06) ◽  
pp. 2865-2865 ◽  
Author(s):  
Karsten Grove ◽  
Wolfgang Ziller
Keyword(s):  
Group Actions ◽  
Nonnegative Curvature

Supersingularity from group actions

2008 ◽  
Vol 281 (4) ◽  
pp. 575-581
Author(s):  
Riccardo Re
Keyword(s):  
Group Actions

I. The Cortes of Castile

1956 ◽  
Vol 12 (3) ◽  
pp. 223-233 ◽  
Author(s):  
Lesley Byrd Simpson
Keyword(s):  
Collective Behavior ◽  
Group Actions ◽  
The Self ◽  
Short Account ◽  
History Of

This will be a short account of the origin, growth, and death of the great parliament of Castile, the Cortes. That sounds a bit dramatic, but there’s nothing to be done about it, for the history of the Cortes of Castile has the elements of a proper tragedy: the self-destruction of a nation by pride, parochialism, and arrogance. One of my colleagues, now deceased, used to account for the aberrations of Spanish collective behavior by ascribing them to “Spanish individualism.” I can only guess that what he had in mind was that Spaniards, when they act in groups, act differently from the rest of us—in which he was certainly correct. Now, when group actions become consistent, formalized, and ritualistic, I call that pattern of conduct an institution, regardless of whether or not someone has taken the trouble to codify it. Institutions, then, have their origin and their being in the minds of men acting collectively.

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