# Algebraic models of the real affine plane

Abstract : 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 real affine plane, contrary to the compact case.
Keywords :
Type de document :
Pré-publication, Document de travail
2017

https://hal.archives-ouvertes.fr/hal-01578348
Soumis le : mardi 29 août 2017 - 09:47:35
Dernière modification le : vendredi 8 juin 2018 - 14:50:07

### Identifiants

• HAL Id : hal-01578348, version 1
• ARXIV : 1708.08058

### Citation

Adrien Dubouloz, Jérémy Blanc. Algebraic models of the real affine plane . 2017. 〈hal-01578348〉

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