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Pré-Publication, Document De Travail Année : 2017

Algebraic models of the real affine plane

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 real affine plane, contrary to the compact case.

Dates et versions

hal-01578348 , version 1 (29-08-2017)

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