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Transactions of the American Mathematical Society

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Rational quintics in the real plane


Authors: Ilia Itenberg, Grigory Mikhalkin and Johannes Rau
Journal: Trans. Amer. Math. Soc. 370 (2018), 131-196
MSC (2010): Primary 14P25, 14T05
DOI: https://doi.org/10.1090/tran/6938
Published electronically: June 21, 2017
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Abstract: From a topological viewpoint, a rational curve in the real projective plane is generically a smoothly immersed circle and a finite collection of isolated points. We give an isotopy classification of generic rational quintics in $ \mathbb{RP}^2$ in the spirit of Hilbert's 16th problem.


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Ilia Itenberg
Affiliation: Université Pierre et Marie Curie, Institut de Mathématiques de Jussieu - Paris Rive Gauche, 4 place Jussieu, 75252 Paris Cedex 5, France — and — Département de Mathématiques et Applications, École Normale Supérieure, 45 rue d’Ulm, 75230 Paris Cedex 5, France
Email: ilia.itenberg@imj-prg.fr

Grigory Mikhalkin
Affiliation: Section de Mathématiques, Université de Genève, Battelle Villa, 1227 Carouge, Suisse
Email: grigory.mikhalkin@unige.ch

Johannes Rau
Affiliation: Fachrichtung Mathematik, Universität der Saarlandes, Postfach 151150, 66041 Saarbrücken, Germany
Address at time of publication: Fachbereich Mathematik, Eberhard Karls Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany
Email: johannes.rau@math.uni-tuebingen.de

DOI: https://doi.org/10.1090/tran/6938
Received by editor(s): October 9, 2015
Received by editor(s) in revised form: March 9, 2016
Published electronically: June 21, 2017
Additional Notes: Part of the research was conducted during the stay of all three authors at the Max-Planck-Institut für Mathematik in Bonn. Research was supported in part by the FRG Collaborative Research grant DMS-1265228 of the U.S. National Science Foundation (first author), the grants 141329, 159240 and the NCCR SwissMAP project of the Swiss National Science Foundation (second author)
Article copyright: © Copyright 2017 American Mathematical Society

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