scholarly journals Linear equations on real algebraic surfaces

2017 ◽  
Vol 154 (3-4) ◽  
pp. 285-296 ◽  
Author(s):  
Wojciech Kucharz ◽  
Krzysztof Kurdyka
Keyword(s):  
Linear Equations ◽  
Algebraic Surfaces ◽  
Real Algebraic Surfaces

scholarly journals Geometrically rational real conic bundles and very transitive actions

2010 ◽  
Vol 147 (1) ◽  
pp. 161-187 ◽  
Author(s):  
Jérémy Blanc ◽  
Frédéric Mangolte
Keyword(s):  
Automorphism Groups ◽  
Algebraic Surfaces ◽  
Algebraic Models ◽  
Transitive Automorphism ◽  
Real Locus ◽  
Real Algebraic Surfaces ◽  
Conic Bundles ◽  
Transitive Actions ◽  
Insight Into

AbstractIn this article we study the transitivity of the group of automorphisms of real algebraic surfaces. We characterize real algebraic surfaces with very transitive automorphism groups. We give applications to the classification of real algebraic models of compact surfaces: these applications yield new insight into the geometry of the real locus, proving several surprising facts on this geometry. This geometry can be thought of as a half-way point between the biregular and birational geometries.

scholarly journals On the geometric structure of certain real algebraic surfaces

2017 ◽  
Vol 191 (1) ◽  
pp. 153-169
Author(s):  
Miguel Angel Guadarrama-García ◽  
Adriana Ortiz-Rodríguez
Keyword(s):  
Geometric Structure ◽  
Algebraic Surfaces ◽  
Real Algebraic Surfaces

scholarly journals Symplectic bilinear forms on affine real algebraic surfaces

1989 ◽  
Vol 31 (2) ◽  
pp. 195-198
Author(s):  
W. Kucharz
Keyword(s):  
Commutative Ring ◽  
Algebraic Surfaces ◽  
Bilinear Forms ◽  
Witt Group ◽  
Real Algebraic Surfaces ◽  
Definition Of

Given a commutative ring A with identity, let W–1(A) denote the Witt group of skew-symmetric bilinear forms over A (cf. [1] or [7] for the definition of W–1 (A)).

scholarly journals Algebraic models of the Euclidean plane

2018 ◽  
Vol Volume 2 ◽  
Author(s):  
Jérémy Blanc ◽  
Adrien Dubouloz
Keyword(s):  
Euclidean Plane ◽  
Kodaira Dimension ◽  
Algebraic Surfaces ◽  
Algebraic Models ◽  
The Real ◽  
Homology Groups ◽  
Real Algebraic Surfaces ◽  
Compact Case ◽  
Birational Diffeomorphism

We introduce a new invariant, the real (logarithmic)-Kodaira dimension, that allows to distinguish smooth real algebraic surfaces up to birational diffeomorphism. As an application, we construct infinite families of smooth rational real algebraic surfaces with trivial homology groups, whose real loci are diffeomorphic to $\mathbb{R}^2$, but which are pairwise not birationally diffeomorphic. There are thus infinitely many non-trivial models of the euclidean plane, contrary to the compact case. Comment: 16 pages

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