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Algebraic models of the line in the real affine plane

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.
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https://hal.archives-ouvertes.fr/hal-01802038
Contributor : Frédéric Mangolte <>
Submitted on : Wednesday, January 8, 2020 - 2:33:42 PM
Last modification on : Thursday, January 28, 2021 - 10:28:03 AM
Long-term archiving on: : Thursday, April 9, 2020 - 1:10:52 PM

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Adrien Dubouloz, Frédéric Mangolte. Algebraic models of the line in the real affine plane. Geometriae Dedicata, Springer Verlag, 2021, 210, pp.179-204. ⟨10.1007/s10711-020-00539-1⟩. ⟨hal-01802038v2⟩

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