10.46298/epiga.2018.volume2.4511
https://epiga.episciences.org/4511
Blanc, Jérémy
Jérémy
Blanc
Dubouloz, Adrien
Adrien
Dubouloz
Algebraic models of the Euclidean plane
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.
Comment: 16 pages
episciences.org
Mathematics - Algebraic Geometry
Mathematics - Differential Geometry
14R05 14R25 14E05 14P25 14J26
2018-12-04
2018-12-05
2018-12-05
eng
journal article
arXiv:1708.08058
10.48550/arXiv.1708.08058
2491-6765
https://epiga.episciences.org/4511/pdf
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Épijournal de Géométrie Algébrique
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