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Documents  14R25 | enregistrements trouvés : 3

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- 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

14-06 ; 14R20 ; 14R10 ; 14E07 ; 14J26 ; 05E18 ; 14E05 ; 14E30 ; 14J10 ; 14J45 ; 14M17 ; 14M25 ; 13A50 ; 14D07 ; 14H50 ; 14J50 ; 14L10 ; 14L30 ; 14R05 ; 14R25 ; 20E06 ; 20F55 ; 32G20 ; 32M12 ; 52B20

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Research talks

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.
(Joint Work with Adrien Dubouloz).
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 ...

14R05 ; 14R25 ; 14E05 ; 14P25 ; 14J26

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- 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

12Exx ; 13A50 ; 14J50 ; 14L24 ; 14L30 ; 14M17 ; 14R25 ; 14R10 ; 16S32 ; 17B45 ; 20Cxx ; 20G05 ; 20G20 ; 20H15 ; 22E15 ; 22E46 ; 32M05 ; 53C55 ; 53C35 ; 53D20 ; 14-06 ; 13-06

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