Pierre-Marie Poloni
Since September 2009, I am a post-doc assistant at the Mathematics Institute of the University of Basel.
Contact information
Mathematisches Institut
Universität Basel
Rheinsprung 21
CH-4051 Basel
Switzerland |
Büro: 23
Tel: +41 (0)61 267 26 94
Email: pierre-marie.poloni "AT" unibas.ch
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Research interests
I work in Affine Algebraic Geometry and I am specifically interested in
the following topics:
- Affine surfaces with additive group actions (notably Danielewski surfaces)
- Polynomial automorphisms of affine spaces
- Embedding Problem, Abhyankar-Sathaye Conjecture and Cancellation Problem
- Exotic algebraic structures on affine spaces
- Locally nilpotent derivations
Publications and preprints
- (with A. Dubouloz and L. Moser-Jauslin) Noncancellation for smooth contractible affine threefolds,
Proc. Amer. Math. Soc. 139 (2011), 4273-4284. [Preprint version]
- Classification(s) of Danielewski hypersurfaces,
Transformation Groups, Volume 16, Issue 2 (2011), 579-597.
DOI: 10.1007/s00031-011-9146-5 . [Preprint version]
- (with A. Dubouloz and L. Moser-Jauslin) Inequivalent embeddings of the Koras-Russell cubic threefold,
Michigan Mathematical Journal, Volume 59, Issue 3 (2010), 679-694. [Preprint version]
- (with S. Maubach) The Nagata automorphism is shifted
linearizable,
Journal of Algebra, 321 (2009), p. 879-889 [Preprint version]
- Embeddings of a family of
Danielewski hypersurfaces (abstract of the talk I gave during the workshop Affine
Algebraic Geometry),
Oberwolfach Reports, vol.4, n°1, 2007.[Preprint version]
- (with A. Dubouloz) On a class of Danielewski surfaces in affine 3-space,
Journal of Algebra, 321 (2009), p. 1797-1812 [Preprint version]
- (with L. Moser-Jauslin) Embeddings of a family of Danielewski hypersurfaces and certain C^+-actions on C^3,
Annales de l'institut Fourier, 56 n°5 (2006), p. 1567-1581. [Preprint version]
Ph.D. Thesis
I have defended my Ph.D. Thesis "Sur les plongements des hypersurfaces de Danielewski" on June 2008 at the Institut de Mathématiques de Bourgogne.
The manuscript (in french) is available here or on the TEL server.
Links
Seminar Algebra and Geometry of the mathematics institute of Basel.
Workgroup Automorphisms of affine spaces (in french).
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