Pierre-Marie 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.)
  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