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Mathematics > Algebraic Geometry

arXiv:1805.11406 (math)
[Submitted on 29 May 2018 (v1), last revised 13 Jan 2020 (this version, v2)]

Title:Algebraic models of the line in the real affine plane

Authors:Adrien Dubouloz (IMB), Frédéric Mangolte (LAREMA)
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Abstract:We study smooth rational closed embeddings of the real affine line into the real affine plane, that is algebraic rational maps from the real affine line to the real affine plane which induce smooth closed embeddings of the real euclidean line into the real euclidean plane. We consider these up to equivalence under the group of birational automorphisms of the real affine plane which are diffeomorphisms of its real locus. We show that in contrast with the situation in the categories of smooth manifolds with smooth maps and of real algebraic varieties with regular maps where there is only one equivalence class up to isomorphism, there are non-equivalent smooth rational closed embeddings up to such birational diffeomorphisms.
Subjects: Algebraic Geometry (math.AG)
Cite as: arXiv:1805.11406 [math.AG]
  (or arXiv:1805.11406v2 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1805.11406
Related DOI: https://doi.org/10.1007/s10711-020-00539-1

Submission history

From: Frederic Mangolte [view email] [via CCSD proxy]
[v1] Tue, 29 May 2018 13:06:11 UTC (45 KB)
[v2] Mon, 13 Jan 2020 09:19:14 UTC (407 KB)
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