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The decomposition group of a line in the plane


Authors: Isac Hedén and Susanna Zimmermann
Journal: Proc. Amer. Math. Soc. 145 (2017), 3665-3680
MSC (2010): Primary 14E07
DOI: https://doi.org/10.1090/proc/13263
Published electronically: May 24, 2017
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Abstract: We show that the decomposition group of a line $ L$ in the plane, i.e., the subgroup of plane birational transformations that send $ L$ to itself birationally, is generated by its elements of degree 1 and one element of degree 2, and that it does not decompose as a non-trivial amalgamated product.


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Additional Information

Isac Hedén
Affiliation: Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502 Japan
Email: Isac.Heden@kurims.kyoto-u.ac.jp

Susanna Zimmermann
Affiliation: Departement Mathematik und Informatik, Universität Basel, Spiegelgasse 1, 4051 Basel, Switzerland
Email: Susanna.Zimmermann@unibas.ch

DOI: https://doi.org/10.1090/proc/13263
Received by editor(s): January 29, 2016
Received by editor(s) in revised form: April 21, 2016
Published electronically: May 24, 2017
Additional Notes: The first-named author is an International Research Fellow of the Japanese Society for the Promotion of Sciences, and this work was supported by Grant-in-Aid for JSPS Fellows Number 15F15751. Both authors acknowledge support by the Swiss National Science Foundation Grant “Birational Geometry” PP00P2_153026.
Communicated by: Lev Borisov
Article copyright: © Copyright 2017 American Mathematical Society

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