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Algebraic models of the Euclidean plane
Auteur(s)
Adrien Dubouloz
Date de parution
2018
In
Épijournal de Géométrie Algébrique
Vol.
2
Résumé
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.
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.
Identifiants
Type de publication
journal article
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