Adrien Dubouloz

Chargé de Recherches - Université de Bourgogne - CNRS

Recent Preprints
  1. $\mathbb{A}^2$-fibrations between affine spaces are trivial $\mathbb{A}^2$-bundles arXiv:1704.04440. Abstract
  2. The equivariant Jacobian Conjecture fails for pseudo-planes, with Karol Palka arXiv:1701.01425. Abstract
  1. Cylinders in del Pezzo fibrations, with Takashi Kishimoto,
    Isral J. Math. (to appear) arXiv:1607.00840. Abstract
  2. Fake Real Planes: exotic affine algebraic models of $\mathbb{R}^{2}$ , with Frédéric Mangolte,
    Selecta Math. (to appear), arXiv:1507.01574. Abstract
  3. Affine lines in the complement of a smooth plane conic, with Julie Decaup
    Bollettino dell'Unione Matematica Italiana (to appear), arXiv:1611.03248. Abstract
  4. Families of exotic affine 3-spheres,
    European Journal of Mathematics (to appear) arXiv:1610.01409. Abstract
  5. Affine surfaces with isomorphic $\mathbb{A}^2$-cylinders,
    Kyoto J. Maths (to appear), arXiv:1507.05802. Abstract
  6. Families of $\mathbb{A}^1$-contractible affine threefolds, with Jean Fasel,
    Algebraic Geometry (to appear), arXiv:1512.01933. Abstract
  7. Explicit biregular/birational geometry of affine threefolds: completions of $\mathbb{A}^3$ into del pezzo fibrations and Mori conic bundles, with Takashi Kishimoto,
    Adv. Stud. Pure Math., Mathematical Society of Japan, Tokyo (to appear), arXiv:1508.01792. Abstract
  8. Affine-ruled varieties without the Laurent cancellation property, with Pierre-Marie Poloni,
    Bull. London Math. Soc. (2016) 48 (5): 822-834. arXiv:1509.07803. Abstract
  9. Rationally integrable vector fields and rational additive group actions, with Alvaro Liendo,
    International J. of Math. Vol. 27, No. 8 (2016) 1650060. arXiv:1409.5878. Abstract
  10. On the cancellation problem for algebraic tori,
    Ann. Inst. Fourier Vol. 66 (6) (2016), 2621-2640. arXiv:1412.2213. Abstract
  11. Real Frontiers of Fake Planes, with Frédéric Mangolte,
    European Journal of Mathematics, 2(1) (2016), 140-168. arXiv:1508.07695. Abstract
  12. Families of affine ruled surfaces: existence of cylinders, with Takashi Kishimoto,
    Nagoya Mathematical Journal, Vol 223 (1) (2016), 1-20. arXiv:1408.1328. Abstract
  13. Flexible bundles over rigid affine surfaces,
    Comment. Math. Helv. 90 (2015), 121-137. arXiv:1304.4189.
  14. Log-uniruled affine varieties without cylinder-like open subsets, with Takashi Kishimoto,
    Bull. Soc. math. France, 143 (1), 2015, 383-401. arXiv:1212.0521.
  15. Complements of hyperplane sub-bundles in projective spaces bundles over $ \mathbb{P}^1 $,
    Math. Ann. 361 (2015), no 1-2, 259–273. arXiv:1108.6209.
  16. Affine Surfaces With a Huge Group of Automorphisms, with Jérémy Blanc,
    Int. Math. Res. Notices, 2015 (2), 422-459. arXiv:1302.3813.
  17. Automorphisms of open surfaces with irreducible boundary, with Stéphane Lamy,
    Osaka J. Math. Volume 52, Number 3 (2015), 747-793. arXiv:1404.4838.
  18. Proper triangular $\mathbb{G}_a$-actions on $\mathbb{A}^4$ are translations, with David R. Finston and Imad Jaradat,
    Algebra Number Theory 8 (2014), no. 8, 1959–1984. arXiv:1303.1032.
  19. On exotic affine 3-spheres, with David R. Finston,
    J. Algebraic Geom. 23 (2014), no. 3, 445–469. arXiv:1106.2900.
  20. Proper twin-triangular $\mathbb{G}_a$-actions on $\mathbb{A}^4$ are translations, with David R. Finston,
    Proc. Amer. Math. Soc. 142 (2014), no. 5, 1513–1526. arXiv:1109.6302.
  21. Equivariant triviality of quasi-monomial triangular $\mathbb{G}_a$-actions on $\mathbb{A}^4$, with David R. Finston and Imad Jaradat,
    in "Automorphisms in Birational and Affine Geometry" Proceedings of conference in Levico Terme, Italy, October, 2012,
    Springer Proceedings in Mathematics and Statistics, (2014).
  22. Automorphism groups of certain rational hypersurfaces in complex four-space, with Lucy Moser-Jauslin and Pierre-Marie Poloni,
    in "Automorphisms in Birational and Affine Geometry" Proceedings of conference in Levico Terme, Italy, October, 2012,
    Springer Proceedings in Mathematics and Statistics, (2014). arXiv:1309.7363.
  23. Affine open subsets in $\mathbb{A}^3$ without the cancellation property,
    in "Commutative algebra and algebraic geometry" (CAAG-2010), 63–67, Ramanujan Math. Soc. Lect. Notes Ser., 17, Ramanujan Math. Soc., Mysore, 2013. arXiv:1107.1968.
  24. Locally tame plane polynomial automorphisms , with Joost Berson, Jean-Philippe Furter and Stefan Maubach,
    Journal of Pure and Applied Algebra 216 (2012) 149­-153. arXiv:1011.0976.
  25. Non cancellation for smooth contractible threefolds, with Lucy Moser-Jauslin and Pierre-Marie Poloni,
    Proc. Amer. Math. Soc. 139 (2011) 4273-4284. arXiv:1004.4723.
  26. Automorphisms of $\mathbb{A}^1$-fibered surfaces, with Jérémy Blanc,
    Trans. Amer. Math. Soc. 363 (2011), 5887-5924. arXiv:0906.3623v1.
  27. Inequivalent embeddings of the Koras-Russell cubic threefold, with Lucy Moser-Jauslin and Pierre-Marie Poloni,
    Michigan Mathematical Journal, Volume 59, no. 3 (2010), p. 679-694. arXiv:0903.4278v1.
  28. 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.
  29. On a class of Danielewski surfaces in affine 3-space , with Pierre-Marie Poloni,
    Journal of Algebra 321 (2009), p.1797-1812. arXiv:math/0602549.
  30. Additive group actions on Danielewski varieties and the Cancellation Problem,
    Math. Z. 255 (2007), no. 1, p. 77-93. arXiv:math/0507505v1.
  31. Embeddings of Danielewski surfaces in affine spaces,
    Commentarii Mathematici Helvetici vol 81, no. 1, (2006), p. 49-73. arXiv:math/0403208.
  32. Danielewski-Fieseler surfaces,
    Transformation Groups vol. 10, no. 2, (2005), p. 139-162. arXiv:math/0401225.
  33. Completions of normal affine surfaces with a trivial Makar-Limanov invariant,
    Michigan Mathematical Journal vol. 52, no. 2, (2004), p. 289-308.
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Other Texts, not intended to be published
  1. Factorial threefolds with $\mathbb{G}_a$-actions, with David R. Finston and Parag Deepak Mehta, arXiv:0902.3873, (2009), 14p.
  2. Variations on the log-Sarkisov program for surfaces, with Stéphane Lamy, arXiv:0802.2441, (2008), 26p.
  3. Autour d'une surface rationnelle dans $\mathbb{C}^3$, math.AG/0512152, (2005), 14p.
  4. Quelques remarques sur la notion de modification affine, math.AG/0503142, (2005), 5p.
  5. Sur une classe de schémas avec actions de fibrés en droites, Ph. D. Thesis, Université Grenoble I (2004), 220p.
    Available (in French !) here: tel-00007733.
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