PierreMarie Poloni
Email: poloni.pierremarie "AT" gmail.com
Research interests Affine algebraic geometry, and more specifically:
 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
(Preprint versions may differ slightly from published papers.)
 Complements of hypersurfaces in projective spaces,
with Jérémy Blanc and Immanuel van Santen
preprint https://arxiv.org/abs/2301.13040
 Real forms of some Gizatullin surfaces and KorasRussell threefolds,
with Jérémy Blanc and Anna Bot
to appear in Publicacions Matemàtiques. https://arxiv.org/abs/2108.12389
 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
 Isomorphisms between cylinders over Danielewski surfaces,
with Lucy MoserJauslin
Beitr. Algebra Geom. 62 (2021), 755–771. Official webpage or https://arxiv.org/abs/2002.12202
 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
 On the maximality of the triangular subgroup,
with JeanPhilippe Furter Annales de l'institut Fourier, 68 no. 1 (2018), p. 393–421. Official webpage
 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
 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
 Affineruled 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
 On the closure of the tame automorphism group of affine threespace,
with Eric Edo Int. Math. Res. Not. (IMRN), 2015, no. 19, 9736–9750. Official webpage or https://arxiv.org/abs/1403.2843
 Automorphism groups of certain rational hypersurfaces in complex fourspace,
with Adrien Dubouloz and Lucy MoserJauslin
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
 A note on the stable equivalence problem,
J. Math. Soc. Japan 67 (2015), no. 2, 753–761. Official webpage
 Extension of automorphisms of rational smooth affine curves,
with Jérémy Blanc and JeanPhilippe Furter Math. Res. Lett. 23 (2016), no. 1, 43–66. Official webpage
 Noncancellation for smooth contractible affine threefolds,
with Adrien Dubouloz and Lucy MoserJauslin
Proc. Amer. Math. Soc. 139 (2011), 4273–4284. Official webpage
 Classification(s) of Danielewski hypersurfaces,
Transformation Groups, Volume 16, Issue 2 (2011), 579–597. Official webpage or https://arxiv.org/abs/0912.3241
 Inequivalent embeddings of the KorasRussell cubic threefold,
with Adrien Dubouloz and Lucy MoserJauslin
Michigan Mathematical Journal, Volume 59, Issue 3 (2010), 679–694. Official webpage
 The Nagata automorphism is shifted linearizable,
with Stefan Maubach
Journal of Algebra, 321 (2009), p. 879–889. Official webpage
 On a class of Danielewski surfaces in affine 3space,
with Adrien Dubouloz
Journal of Algebra, 321 (2009), p. 1797–1812. Official webpage
 Embeddings of a family of Danielewski hypersurfaces and certain C^+actions on C^3,
with Lucy MoserJauslin
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 nâ€™admet pas de forme réelle non triviale.
 November 2021, BaselEPFLDijon Seminar , Basel, Switzerland. Real forms of affine algebraic varieties: two examples.
 July 2019, 1st Joint Meeting BrazilFrance 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 MoserJauslin , 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 contreexemples 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 SwissFrench 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, MiniWorkshop Analytic and Algebraic Geometry, Bern, Switzerland. Counterexamples to the complement problem.
 December 2015, DijonBasel 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 ShortSchool/Conference on Affine Algebraic Geometry & the Jacobian Conjecture, Chern Institute of Mathematics, Tianjin, China. The tame automorphism subgroup of affine threespace is not closed.
