Algebraic models of the line in the real affine plane
Frédéric MANGOLTE
I2M, Aix-Marseille Université
/user/frederic.mangolte/
Date(s) : 03/02/2022 iCal
14h00 - 15h00
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 R into R^2, is equivalent, up to a birational diffeomorphism of the plane, to the linear one?
In this setting, we show that there exists non-equivalent smooth rational closed embeddings up to birational diffeomorphisms. Some of them are simply detected by the non-negativity of the real Kodaira dimension of the complement of their images. This new invariant is derived from topological properties of some « fake real planes » associated with such embeddings.
(Joint Work with Adrien Dubouloz.)
Les modèles algébriques de la droite dans le plan affine réel.
Emplacement
Saint-Charles - FRUMAM (2ème étage)
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