## Blanc, Jérémy and Dubouloz, Adrien - Algebraic models of the Euclidean plane

epiga:4511 - Épijournal de Géométrie Algébrique, 5 décembre 2018, Volume 2
Algebraic models of the Euclidean plane

Auteurs : Blanc, Jérémy and Dubouloz, Adrien

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.

Source : oai:arXiv.org:1708.08058
Volume : Volume 2
Publié le : 5 décembre 2018
Déposé le : 16 mai 2018
Mots-clés : Mathematics - Algebraic Geometry,Mathematics - Differential Geometry,14R05 14R25 14E05 14P25 14J26