Topological affine spaces

1989 ◽  
Vol 35 (1-2) ◽  
pp. 193-198 ◽  
Author(s):  
Corrado Zanella
Keyword(s):  
Affine Spaces ◽  
Topological Affine

Master-Key Leakage-Resilient and Continue Leakage-Resilient Functional Encryption in Dual Affine Spaces

2012 ◽  
Vol 35 (9) ◽  
pp. 1856
Author(s):  
Ming-Wu ZHANG ◽  
Bo YANG ◽  
Tsuyoshi TAKAGI
Keyword(s):  
Functional Encryption ◽  
Affine Spaces ◽  
Dual Affine ◽  
Leakage Resilient ◽  
Key Leakage

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.

Quadrics in Affine Spaces

2018 ◽  
pp. 138-148
Keyword(s):  
Affine Spaces

A Vector and Affine Spaces

2008 ◽  
pp. 707-716
Keyword(s):  
Affine Spaces

More on Real Affine Spaces

2014 ◽  
pp. 119-136
Author(s):  
Francis Borceux
Keyword(s):  
Affine Spaces ◽  
Real Affine

Affine Spaces

2011 ◽  
pp. 1-46
Author(s):  
Agustí Reventós Tarrida
Keyword(s):  
Affine Spaces

scholarly journals Topological affine quadrangles

2005 ◽  
Vol 1 (1) ◽  
pp. 143-169 ◽  
Author(s):  
Nils Rosehr
Keyword(s):  
Topological Affine

scholarly journals A note on the ADHM description of Quot schemes of points on affine spaces

2021 ◽  
Author(s):  
Abdelmoubine A. Henni ◽  
Douglas M. Guimaraes
Keyword(s):  
Affine Spaces ◽  
Quot Schemes

scholarly journals Dynamical degrees of affine-triangular automorphisms of affine spaces

2021 ◽  
pp. 1-42
Author(s):  
JÉRÉMY BLANC ◽  
IMMANUEL VAN SANTEN
Keyword(s):  
Affine Space ◽  
Affine Spaces ◽  
Dynamical Degree ◽  
Perron Number ◽  
Dynamical Degrees ◽  
Affine Automorphism

Abstract We study the possible dynamical degrees of automorphisms of the affine space $\mathbb {A}^n$ . In dimension $n=3$ , we determine all dynamical degrees arising from the composition of an affine automorphism with a triangular one. This generalizes the easier case of shift-like automorphisms which can be studied in any dimension. We also prove that each weak Perron number is the dynamical degree of an affine-triangular automorphism of the affine space $\mathbb {A}^n$ for some n, and we give the best possible n for quadratic integers, which is either $3$ or $4$ .

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