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Peer-reviewedCC BYJournal of the European Mathematical Society

On the dynamical Manin–Mumford conjecture for plane polynomial maps

  • Romain Dujardin1,2,3,4
  • Charles Favre5,2,3,4
  • Matteo Ruggiero6,2,3,4
6 affiliations
  1. 1Sorbonne Université et Université Paris-Cité, France
  2. 2CNRS -Centre de Mathématiques Laurent Schwartz, École Polytechnique, 91128 Palaiseau Cedex, France
  3. 3Sorbonne Université, Laboratoire de probabilités, statistique et modélisation, UMR 8001, 4 place Jussieu, 75005 Paris, France
  4. 4Université de Paris and Sorbonne Université, CNRS, Institut de Mathématiques de Jussieu-Paris Rive Gauche, F-75006 Paris, France
  5. 5École Polytechnique, Palaiseau, France
  6. 6Université Paris-Cité et Sorbonne Université, France
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Abstract

We prove the dynamical Manin–Mumford conjecture for regular polynomial maps of \mathbb{A}^{2} and irreducible curves avoiding superattracting orbits at infinity, over any field of characteristic zero.

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Cite

BibTeXRIS
BibTeX
@article{dujardin2026dynamical,
  title = {{On the dynamical Manin–Mumford conjecture for plane polynomial maps}},
  author = {Romain Dujardin and Charles Favre and Matteo Ruggiero},
  journal = {Journal of the European Mathematical Society},
  year = {2026},
  month = jul,
  doi = {10.4171/jems/1807},
  eprint = {2312.14817},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05762075v1},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - On the dynamical Manin–Mumford conjecture for plane polynomial maps
AU  - Romain Dujardin
AU  - Charles Favre
AU  - Matteo Ruggiero
PY  - 2026
DA  - 2026/07/14
JO  - Journal of the European Mathematical Society
DO  - 10.4171/jems/1807
UR  - https://hal.science/hal-05762075v1
AB  - We prove the dynamical Manin–Mumford conjecture for regular polynomial maps of \mathbb{A}^{2} and irreducible curves avoiding superattracting orbits at infinity, over any field of characteristic zero.
SN  - 1435-9855
SN  - 1435-9863
ER  -