Pierre-Marie Poloni

Research interests

• Embedding problems and extension of automorphisms
• Exotic algebraic structures on affine spaces
• Cancellation Problem
• Polynomial automorphisms of affine spaces
• Locally nilpotent derivations

Publications and preprints

1. Complements of hypersurfaces in projective spaces,
   with Jérémy Blanc and Immanuel van Santen
   preprint https://arxiv.org/abs/2301.13040


2. Real forms of some Gizatullin surfaces and Koras-Russell threefolds,
   with Jérémy Blanc and Anna Bot
   to appear in Publicacions Matemàtiques. https://arxiv.org/abs/2108.12389


3. Bivariables and Vénéreau polynomials,
   with Jérémy Blanc
   Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 31 (2022) no. 5, pp. 1391–1418. Official webpage


4. Isomorphisms between cylinders over Danielewski surfaces,
   with Lucy Moser-Jauslin
   Beitr. Algebra Geom. 62 (2021), 755–771. Official webpage or https://arxiv.org/abs/2002.12202


5. Embedding Riemann surfaces with isolated punctures into the complex plane,
   with Frank Kutzschebauch
   Proc. Amer. Math. Soc. 148 (2020), 4831–4835. Official webpage or https://arxiv.org/abs/1811.08157


6. On the maximality of the triangular subgroup,
   with Jean-Philippe Furter
   Annales de l'institut Fourier, 68 no. 1 (2018), p. 393–421. Official webpage


7. Counterexamples to the Complement Problem,
   Commentarii Mathematici Helvetici, Volume 94, Issue 3 (2019), pp. 439–444. Official webpage or https://arxiv.org/abs/1605.05169


8. The density property for Gizatullin surfaces completed by four rational curves,
   with Rafael B. Andrist and Frank Kutzschebauch
   Proc. Amer. Math. Soc. 145 (2017), 5097–5108. Official webpage or https://arxiv.org/abs/1510.08771


9. Affine-ruled varieties without the Laurent cancellation property,
   with Adrien Dubouloz
   Bull. London Math. Soc. (2016), Volume 48, Issue 5, 822–834. Official webpage or https://arxiv.org/abs/1509.07803


10. On the closure of the tame automorphism group of affine three-space,
    with Eric Edo
    Int. Math. Res. Not. (IMRN), 2015, no. 19, 9736–9750. Official webpage or https://arxiv.org/abs/1403.2843


11. Automorphism groups of certain rational hypersurfaces in complex four-space,
    with Adrien Dubouloz and Lucy Moser-Jauslin
    in (refereed) Proceedings of the GABAG2012 conference: Automorphisms in Birational and Affine Geometry, Springer Proc. Math. Stat., Volume 79 (2014), 301–312. Official webpage or https://arxiv.org/abs/1309.7363


12. A note on the stable equivalence problem,
    J. Math. Soc. Japan 67 (2015), no. 2, 753–761. Official webpage


13. Extension of automorphisms of rational smooth affine curves,
    with Jérémy Blanc and Jean-Philippe Furter
    Math. Res. Lett. 23 (2016), no. 1, 43–66. Official webpage


14. Noncancellation for smooth contractible affine threefolds,
    with Adrien Dubouloz and Lucy Moser-Jauslin
    Proc. Amer. Math. Soc. 139 (2011), 4273–4284. Official webpage


15. Classification(s) of Danielewski hypersurfaces,
    Transformation Groups, Volume 16, Issue 2 (2011), 579–597. Official webpage or https://arxiv.org/abs/0912.3241


16. Inequivalent embeddings of the Koras-Russell cubic threefold,
    with Adrien Dubouloz and Lucy Moser-Jauslin
    Michigan Mathematical Journal, Volume 59, Issue 3 (2010), 679–694. Official webpage


17. The Nagata automorphism is shifted linearizable,
    with Stefan Maubach
    Journal of Algebra, 321 (2009), p. 879–889. Official webpage


18. On a class of Danielewski surfaces in affine 3-space,
    with Adrien Dubouloz
    Journal of Algebra, 321 (2009), p. 1797–1812. Official webpage


19. Embeddings of a family of Danielewski hypersurfaces and certain C^+-actions on C^3,
    with Lucy Moser-Jauslin
    Annales de l'institut Fourier, 56 No.5 (2006), p. 1567–1581. Official webpage

Selected recent talks

• April 2022, Séminaires Géométrie, Algèbre, Dynamique et Topologie, IMB, Dijon, France. La cubique de Russell n’admet pas de forme réelle non triviale.


• November 2021, Basel-EPFL-Dijon Seminar , Basel, Switzerland. Real forms of affine algebraic varieties: two examples.


• July 2019, 1st Joint Meeting Brazil-France in Mathematics , Special Session Derivations in Algebra and Geometry, IMPA, Rio de Janeiro, Brazil. Embedding some open Riemann surfaces into the complex plane.


• May 2019, Conference Affine Algebraic Geometry and Transformation Groups- in honor of Lucy Moser-Jauslin , IMB, Dijon. Embedding some open Riemann surfaces into the complex plane.


• May 2018, Algebraic Geometry – Mariusz Koras in memoriam , Warsaw, Poland. Affine plane bundles over the punctured affine plane.


• March 2018, The 16th affine algebraic geometry meeting, Osaka, Japan. Affine plane bundles over the punctured affine plane.


• February 2018, conference Polynomial Rings and Affine Algebraic Geometry, Tokyo Metropolitan University, Tokyo, Japan. Affine plane bundles over the punctured affine plane.


• September 2017, Mathematical Colloquium, Bern, Switzerland. Stably equivalent polynomials and the complement problem.


• April 2017, Séminaire Georges Reeb, Mulhouse, France. Des contre-exemples au problème des complémentaires.


• March 2017, Oberseminar Geometrie, Fribourg, Switzerland. Around the cancellation problem.


• March 2017, The 15th affine algebraic geometry meeting, Osaka, Japan. The Jonquières subgroup is a Borel subgroup.


• January 2017, 6th Swiss-French workshop on algebraic geometry, Charmey, Switzerland. The Jonquières subgroup is a Borel subgroup.


• October 2016, Workshop Complex Affine Geometry, Effective Hyperbolicity, Analysis in honour of Mikhail Zaidenberg, Grenoble, France. Counterexamples to the complement problem.


• October 2016, Workshop Frontiers in Elliptic Holomorphic Geometry, Jevnaker, Norway. Counterexamples to the complement problem.


• May 2016, Mini-Workshop Analytic and Algebraic Geometry, Bern, Switzerland. Counterexamples to the complement problem.


• December 2015, Dijon-Basel Seminar, Dijon, France. Do triangular automorphisms form a maximal subgroup?


• November 2015, Rencontre ANR BirPol et Fondation Del Duca : Groupes de transformations, Rennes, France. Deux exposés de géométrie affine. (two talks)


• October 2015, Coloquio IMAFI, Talca, Chile. Explicit counterexamples to the Laurent cancellation problem.


• March 2015, Seminar Algebra & Geometry, Basel, Switzerland. Explicit counterexamples to the Laurent Cancellation Problem.


• March 2015, Mathematical Colloquium, Bern, Switzerland. Can we cancel indeterminates?


• July 2014, International Short-School/Conference on Affine Algebraic Geometry & the Jacobian Conjecture, Chern Institute of Mathematics, Tianjin, China. The tame automorphism subgroup of affine three-space is not closed.