Adrien Dubouloz Research

Research Interests : Affine Algebraic Geometry

Automorphism groups of noncomplete algebraic surfaces
Polynomial automorphisms of affine spaces
Additive group actions on affine schemes
Principal bundles and the Cancellation Problem
Logarithmic birational geometry
Infinite dimensional algebraic varieties and ind-schemes

Coordinator of the ANR Project 11-JS01-004-01 Birpol "Automorphismes polynomiaux et transformations birationnelles"
French coordinator of the Swiss-French project Germaine de Staël 2012-30 "Groupes de transformations et géométrie birationnelle"

Recent Preprints

With David Finston, Proper twin-triangular G_a-actions on A⁴ are translations
arXiv:1109.6302 hal-00627521

Complements of hyperplane sub-bundles in projective space bundles over P¹
arXiv:1108.6209 hal-00618025

Affine open subsets in A³ without the cancellation property
arXiv:: 1107.1968 hal-00607720

With David R. Finston, On exotic affine 3-spheres
arXiv:1106.2900 hal-00600542

Publications

With J. Berson, J.-P. Furter and S. Maubach, Locally tame plane polynomial automorphisms
Journal of Pure and Applied Algebra 216 (2012) 149-153
arXiv:1011.0976 hal-00531776

With Lucy Moser-Jauslin and Pierre-Marie Poloni, Non cancellation for smooth contractible threefolds
Proc. Amer. Math. Soc. 139 (2011) 4273-4284.
arXiv 1004.4723 hal-00476471

With Jérémy Blanc, Automorphisms of A¹-fibered surfaces
Trans. Amer. Math. Soc. 363 (2011), 5887-5924.
arXiv:0906.3623v1 hal-00396986

With Lucy Moser-Jauslin and Pierre-Marie Poloni, Inequivalent embeddings of the Koras-Russell cubic threefold
Michigan Mathematical Journal, Volume 59, no. 3 (2010), p. 679-694.
arXiv:0903.4278v1 hal-00370741

The cylinder over the Koras-Russell cubic threefold has a trivial Makar-Limanov invariant
Transformation Groups vol 14, no 3 (2009), p. 531-539.
arXiv:0807.4085 hal-00306229

With Pierre-Marie Poloni, On a class of Danielewski surfaces in affine 3-space ,
Journal of Algebra 321 (2009), p.1797-1812.
arXiv:math/0602549 hal-00019635

Additive group actions on Danielewski varieties and the Cancellation Problem,
Math. Z. 255 (2007), no. 1, p. 77-93 .
arXiv:math/0507505v1 hal-00007651

Embeddings of Danielewski surfaces in affine spaces,
Commentarii Mathematici Helvetici vol 81, no. 1, (2006), p. 49-73.

Danielewski-Fieseler surfaces.
Transformation Groups vol. 10, no. 2, (2005), p. 139-162.

Completions of normal affine surfaces with a trivial Makar-Limanov invariant.
Michigan Mathematical Journal vol. 52, no. 2, (2004), p. 289-308.

Older Preprints

With David R. Finston and Parag Deepak Mehta, Factorial threefolds with Ga-actions
arXiv:0902.3873 hal-00363371

With Stéphane Lamy , Variations on the log-Sarkisov program for surfaces
arXiv:0802.2441 hal-00256812

Autour d'une surface rationnelle dans C³ ,
math.AG/0512152 (2005), 14p.

Quelques remarques sur la notion de modification affine,
math.AG/0503142

Links

Homepage of the ANR project BirPol
Homepage of the workgroup Automorphisms of affine spaces" (in french)
Workshop "Polynomial Automorphisms", Dijon 2008
Local workgroup on A¹-topology of schemes : Schedule .

Contact

Telephone : +33- (0)3 80 39 58 74
Fax : +33- (0)3 80 39 58 99
E-mail : adrien.dubouloz"at"u-bourgogne.fr