Pierre-Marie Poloni

Universität Basel
Departement Mathematik und Informatik
Spiegelgasse 1
CH-4051 Basel
Switzerland
Email: pierre-marie.poloni "AT" unibas.ch

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. Isomorphisms between cylinders over Danielewski surfaces,
    with Lucy Moser-Jauslin
    preprint

  2. Embedding Riemann surfaces with isolated punctures into the complex plane,
    with Frank Kutzschebauch
    accepted for publication in Proceedings of the American Mathematical Society

  3. On the maximality of the triangular subgroup,
    with Jean-Philippe Furter
    Annales de l'institut Fourier, 68 no. 1 (2018), p. 393–421. [Preprint version]

  4. Counterexamples to the Complement Problem,
    Commentarii Mathematici Helvetici, Volume 94, Issue 3 (2019), pp. 439–444. [Preprint version]

  5. 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. [Preprint version]

  6. Affine-ruled varieties without the Laurent cancellation property,
    with Adrien Dubouloz
    Bull. London Math. Soc. (2016), Volume 48, Issue 5, 822–834. [Preprint version]

  7. 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. [Preprint version]

  8. 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. [Preprint version]

  9. A note on the stable equivalence problem,
    J. Math. Soc. Japan 67 (2015), no. 2, 753–761. [Preprint version]

  10. Extension of automorphisms of rational smooth affine curves,
    with Jérémy Blanc and Jean-Philippe Furter
    Math. Res. Lett. 23 (2016), no. 1, 43–66. [Preprint version]

  11. Noncancellation for smooth contractible affine threefolds,
    with Adrien Dubouloz and Lucy Moser-Jauslin
    Proc. Amer. Math. Soc. 139 (2011), 4273–4284. [Preprint version]

  12. Classification(s) of Danielewski hypersurfaces,
    Transformation Groups, Volume 16, Issue 2 (2011), 579–597. [Preprint version]

  13. 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. [Preprint version]

  14. The Nagata automorphism is shifted linearizable,
    with Stefan Maubach
    Journal of Algebra, 321 (2009), p. 879–889. [Preprint version]

  15. On a class of Danielewski surfaces in affine 3-space,
    with Adrien Dubouloz
    Journal of Algebra, 321 (2009), p. 1797–1812. [Preprint version]

  16. 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. [pdf]

Selected recent talks