Jérémy Blanc ; Adrien Dubouloz - Algebraic models of the Euclidean plane

epiga:4511 - Épijournal de Géométrie Algébrique, December 5, 2018, Volume 2 - https://doi.org/10.46298/epiga.2018.volume2.4511
Algebraic models of the Euclidean planeArticle

Authors: Jérémy Blanc ORCID; Adrien Dubouloz

    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.


    Volume: Volume 2
    Published on: December 5, 2018
    Accepted on: November 13, 2018
    Submitted on: May 16, 2018
    Keywords: Mathematics - Algebraic Geometry,Mathematics - Differential Geometry,14R05 14R25 14E05 14P25 14J26
    Funding:
      Source : OpenAIRE Graph
    • Géométrie birationnelle; Funder: Swiss National Science Foundation; Code: 153026

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