Embeddings of affine spaces into quadrics
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- by Jérémy Blanc and Immanuel van Santen PDF
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Abstract:
This article provides, over any field, infinitely many algebraic embeddings of the affine spaces $\mathbb {A}^1$ and $\mathbb {A}^2$ into smooth quadrics of dimension two and three, respectively, which are pairwise non-equivalent under automorphisms of the smooth quadric. Our main tools are the study of the birational morphism $\mathrm {SL}_2 \to \mathbb {A}^3$ and the fibration $\mathrm {SL}_2 \to \mathbb {A}^3 \to \mathbb {A}^1$ obtained by projections, as well as degenerations of variables of polynomial rings, and families of $\mathbb {A}^1$-fibrations.References
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Additional Information
- Jérémy Blanc
- Affiliation: Departement Mathematik und Informatik, Universität Basel, Spiegelgasse 1, CH-4051 Basel, Switzerland
- MR Author ID: 744287
- Email: jeremy.blanc@unibas.ch
- Immanuel van Santen
- Affiliation: Fachbereich Mathematik der Universität Hamburg, Bundesstraße 55, DE-20146 Hamburg, Germany
- Email: immanuel.van.santen@math.ch
- Received by editor(s): March 6, 2017
- Received by editor(s) in revised form: October 10, 2017
- Published electronically: March 28, 2019
- Additional Notes: The second author was born Immanuel Stampfli
- © Copyright 2019 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 371 (2019), 8429-8465
- MSC (2010): Primary 14R10, 14R25, 14J70, 14J50, 14E05
- DOI: https://doi.org/10.1090/tran/7555
- MathSciNet review: 3955552