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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Rational quintics in the real plane
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by Ilia Itenberg, Grigory Mikhalkin and Johannes Rau PDF
Trans. Amer. Math. Soc. 370 (2018), 131-196 Request permission

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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Additional Information
  • 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
  • MR Author ID: 321564
  • 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
  • MR Author ID: 872714
  • Email: johannes.rau@math.uni-tuebingen.de
  • 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)
  • © Copyright 2017 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 370 (2018), 131-196
  • MSC (2010): Primary 14P25, 14T05
  • DOI: https://doi.org/10.1090/tran/6938
  • MathSciNet review: 3717977