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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