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Article Dans Une Revue European Journal of Mathematics Année : 2016

Real frontiers of fake planes

Résumé

In Dubouloz and Mangolte (Fake real planes: exotic affine algebraic models of $\mathbb{R}^{2}$, arXiv:1507.01574, 2015) we define and partially classify fake real planes, that is, minimal complex surfaces with conjugation whose real locus is diffeomorphic to the euclidean real plane $\mathbb{R}^{2}$. Classification results are given up to biregular isomorphisms and up to birational diffeomorphisms. In this note, we describe in an elementary way numerous examples of fake real planes and we exhibit examples of such planes of every Kodaira dimension $\kappa\in \{-\infty,0,1,2\}$ which are birationally diffeomorphic to $\mathbb{R}^{2}$.
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Dates et versions

hal-01188470 , version 1 (30-08-2015)
hal-01188470 , version 2 (10-06-2022)

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Adrien Dubouloz, Frédéric Mangolte. Real frontiers of fake planes. European Journal of Mathematics, 2016, Special Issue: Spitsbergen Volume, 2 (1), pp.140-168. ⟨10.1007/s40879-015-0087-8⟩. ⟨hal-01188470v2⟩
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