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# Documents  14R25 | enregistrements trouvés : 3

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## Algebraic varieties and automorphism groups.Proceedings of the workshop held at RIMSKyoto # July 7-11, 2014 Masuda, Kayo ; Kishimoto, Takashi ; Kojima, Hideo ; Miyanishi, Masayoshi ; Zaidenberg, Mikhail | Mathematical Society of Japan 2017

Congrès

- 474 p.
ISBN 978-4-86497-048-8

Advanced studies in pure mathematics , 0075

Localisation : Collection 1er étage

géométrie algébrique # groupe d'automorphisme # groupe algébrique # variété algébrique # automorphisme birationnel

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## Algebraic models of the line in the real affine plane Mangolte, Frédéric | CIRM H

Multi angle

Algebraic and Complex Geometry

We study the following real version of the famous Abhyankar-Moh Theorem: Which real rational map from the affine line to the affine plane, whose real part is a non-singular real closed embedding of $\mathbb{R}$ into $\mathbb{R}^2$, is equivalent, up to a birational diffeomorphism of the plane, to the linear one? We show that in contrast with the situation in the categories of smooth manifolds with smooth maps and of real algebraic varieties with regular maps where there is only one equivalence class up to isomorphism, there are plenty of non-equivalent smooth rational closed embeddings up to birational diffeomorphisms. Some of these are simply detected by the non-negativity of the real Kodaira dimension of the complement of their images. But we also introduce finer invariants derived from topological properties of suitable fake real planes associated to certain classes of such embeddings.
We study the following real version of the famous Abhyankar-Moh Theorem: Which real rational map from the affine line to the affine plane, whose real part is a non-singular real closed embedding of $\mathbb{R}$ into $\mathbb{R}^2$, is equivalent, up to a birational diffeomorphism of the plane, to the linear one? We show that in contrast with the situation in the categories of smooth manifolds with smooth maps and of real algebraic varieties with ...

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## Symmetry and spaces:in honor of Gerry Schwarz Campbell, H. E. A. ; Helminck, Aloysius G. ; Kraft, Hanspeter ; Wehlau, David | Birkhäuser 2010

Ouvrage

- xx; 207 p.
ISBN 978-0-8176-4874-9

Progress in mathematics , 0278

Localisation : Collection 1er étage

géométrie algébrique # action de groupe # théorie des invariants modulaires

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