Adrien Dubouloz

Chargé de Recherches - Université de Bourgogne - CNRS

Recent Preprints
  1. Normal real affine varieties with circle actions, with Alvaro Liendo, arXiv:1810.11712. Abstract
  2. Algebraic vector bundles on the 2-sphere and smooth rational varieties with infinitely many real forms, with Gene Freudenburg and Lucy Moser-Jauslin, arXiv:1807.05885. Abstract
  3. Algebraic models of the line in the real affine plane, with Frédéric Mangolte, arXiv:1805.11406. Abstract
  4. $\mathbb{A}^1$-contractibility of affine modifications, with Sabrina Pauli and Paul Arne Østvær, arXiv:1805.08959. Abstract
  5. Cylinders in Mori Fiber Spaces: forms of the quintic del Pezzo threefold, with Takashi Kishimoto, arXiv:1805.05679. Abstract
  6. Algebraic models of the real affine plane, with Jérémy Blanc, arXiv:1708.08058. Abstract
  7. Equivariant extensions of $\mathbb{G}_a$-torsors over punctured surfaces, with Isac Hedén and Takashi Kishimoto, arXiv:1707.08768. Abstract
Publications
  1. Deformations of $\mathbb{A}^1$-cylindrical varieties, with Takashi Kishimoto,
    Math. Ann. (to appear), arXiv:1710.09108. Abstract
  2. Super-rigid affine Fano varieties, with Ivan Cheltsov and Jihun Park,
    Compositio Math. vol 154, Issue 11 (2018), 2463-2484, arxiv:1712.09148. Abstract
  3. The Jacobian Conjecture fails for pseudo-planes, with Karol Palka,
    Advances in Math. Volume 339 (2018), 248-284, arXiv:1701.01425. Abstract
  4. Cylinders in del Pezzo fibrations, with Takashi Kishimoto,
    Israël J. Math. Volume 225, Issue 2 (2018), 797-815, arXiv:1607.00840. Abstract
  5. Fake Real Planes: exotic affine algebraic models of $\mathbb{R}^{2}$ , with Frédéric Mangolte,
    Selecta Math., 23(3), 2017, 1619-1668. arXiv:1507.01574. Abstract
  6. Affine lines in the complement of a smooth plane conic, with Julie Decaup
    Boll Unione Mat Ital, Volume 11, Issue 1 (2018), 39–54. arXiv:1611.03248. Abstract
  7. Families of exotic affine 3-spheres,
    European Journal of Mathematics, 4(1) (2018), 212-222. arXiv:1610.01409. Abstract
  8. Affine surfaces with isomorphic $\mathbb{A}^2$-cylinders,
    Kyoto J. Maths (to appear), arXiv:1507.05802. Abstract
  9. Families of $\mathbb{A}^1$-contractible affine threefolds, with Jean Fasel,
    Algebraic Geometry 5 (1) (2018) 1-14. arXiv:1512.01933. Abstract
  10. 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. 75, Mathematical Society of Japan, Tokyo, 2017, 49-71. arXiv:1508.01792. Abstract
  11. 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
  12. 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
  13. On the cancellation problem for algebraic tori,
    Ann. Inst. Fourier Vol. 66 (6) (2016), 2621-2640. arXiv:1412.2213. Abstract
  14. Real Frontiers of Fake Planes, with Frédéric Mangolte,
    European Journal of Mathematics, 2(1) (2016), 140-168. arXiv:1508.07695. Abstract
  15. Families of affine ruled surfaces: existence of cylinders, with Takashi Kishimoto,
    Nagoya Mathematical Journal, Vol 223 (1) (2016), 1-20. arXiv:1408.1328. Abstract
  16. Flexible bundles over rigid affine surfaces,
    Comment. Math. Helv. 90 (2015), 121-137. arXiv:1304.4189.
  17. Log-uniruled affine varieties without cylinder-like open subsets, with Takashi Kishimoto,
    Bull. Soc. math. France, 143 (1), 2015, 383-401. arXiv:1212.0521.
  18. 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.
  19. Affine Surfaces With a Huge Group of Automorphisms, with Jérémy Blanc,
    Int. Math. Res. Notices, 2015 (2), 422-459. arXiv:1302.3813.
  20. Automorphisms of open surfaces with irreducible boundary, with Stéphane Lamy,
    Osaka J. Math. Volume 52, Number 3 (2015), 747-793. arXiv:1404.4838.
  21. 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.
  22. On exotic affine 3-spheres, with David R. Finston,
    J. Algebraic Geom. 23 (2014), no. 3, 445–469. arXiv:1106.2900.
  23. 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.
  24. 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).
  25. 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.
  26. 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.
  27. 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.
  28. 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.
  29. Automorphisms of $\mathbb{A}^1$-fibered surfaces, with Jérémy Blanc,
    Trans. Amer. Math. Soc. 363 (2011), 5887-5924. arXiv:0906.3623v1.
  30. 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.
  31. 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.
  32. 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.
  33. Additive group actions on Danielewski varieties and the Cancellation Problem,
    Math. Z. 255 (2007), no. 1, p. 77-93. arXiv:math/0507505v1.
  34. Embeddings of Danielewski surfaces in affine spaces,
    Commentarii Mathematici Helvetici vol 81, no. 1, (2006), p. 49-73. arXiv:math/0403208.
  35. Danielewski-Fieseler surfaces,
    Transformation Groups vol. 10, no. 2, (2005), p. 139-162. arXiv:math/0401225.
  36. 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. $\mathbb{A}^2$-fibrations between affine spaces are trivial $\mathbb{A}^2$-bundles, arXiv:1704.04440. Abstract
  2. Factorial threefolds with $\mathbb{G}_a$-actions, with David R. Finston and Parag Deepak Mehta, arXiv:0902.3873, (2009), 14p.
  3. Variations on the log-Sarkisov program for surfaces, with Stéphane Lamy, arXiv:0802.2441, (2008), 26p.
  4. Autour d'une surface rationnelle dans $\mathbb{C}^3$, math.AG/0512152, (2005), 14p.
  5. Quelques remarques sur la notion de modification affine, math.AG/0503142, (2005), 5p.
  6. 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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