The Michigan Mathematical Journal

Equivariantly uniformly rational varieties

Charlie Petitjean

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Michigan Math. J., Volume 66, Issue 2 (2017), 245-268.

First available in Project Euclid: 1 June 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14L30: Group actions on varieties or schemes (quotients) [See also 13A50, 14L24, 14M17] 14R20: Group actions on affine varieties [See also 13A50, 14L30]
Secondary: 14M20: Rational and unirational varieties [See also 14E08] 14E08: Rationality questions [See also 14M20]


Petitjean, Charlie. Equivariantly uniformly rational varieties. Michigan Math. J. 66 (2017), no. 2, 245--268. doi:10.1307/mmj/1496282443.

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  • K. Altmann and J. Hausen, Polyhedral divisors and algebraic torus actions, Math. Ann. 334 (2006), no. 3, 557–607.
  • K. Altmann, J. Hausen, and H. Suss, Gluing affine torus actions via divisorial fans, Transform. Groups 13 (2008), no. 2, 215–242.
  • I. Arzhantsev, A. Perepechko, and H. Süss, Infinite transitivity on universal torsors, J. Lond. Math. Soc. (2) 89 (2014), no. 3, 762–778.
  • A. Białynicki-Birula, Remarks on the action of an algebraic torus on $k^{n}$. II, Bull. Acad. Pol. Sci., Sér. Sci. Math. Astron. Phys. 14 (1966), 177–181.
  • G. Bodnàr, H. Hauser, J. Schicho, and O. Villamayor U, Plain varieties, Bull. Lond. Math. Soc. 40 (2008), no. 6, 965–971.
  • F. Bogomolov and C. Böhning, On uniformly rational varieties, Topology, geometry, integrable systems, and mathematical physics, Amer. Math. Soc. Transl. Ser. 2, 234, pp. 33–48, Amer. Math. Soc., Providence, RI, 2014.
  • M. Demazure, Anneaux gradués normaux, Introduction à la théorie des singularités, II, Travaux en Cours, 37, pp. 35–68, Hermann, Paris, 1988.
  • A. Dubouloz, Quelques remarques sur la notion de modification affine..
  • H. Flenner and M. Zaidenberg, Normal affine surfaces with $\mathbb{C}^{*}$-actions, Osaka J. Math. 40 (2003), no. 4, 981–1009.
  • M. Gromov, Oka's principle for holomorphic sections of elliptic bundles, J. Amer. Math. Soc. 2 (1989), no. 4, 851–897.
  • R. Gurjar, M. Koras, and P. Russell, Two dimensional quotients of \noun$\mathbb{C}^{n}$ by a reductive group, Electron. Res. Announc. Math. Sci. 15 (2008), 62–64.
  • A. Gutwirth, The action of an algebraic torus on the affine plane, Trans. Amer. Math. Soc. 105 (1962), 407–414.
  • R. Hartshorne, Algebraic geometry, Grad. Texts in Math., 52, Springer-Verlag, New York–Heidelberg, 1977.
  • S. Kaliman, M. Koras, L. Makar-Limanov, and P. Russell, $\mathbb{C}^{*}$-Actions on $\mathbb{C}^{3}$ are linearisable, Electron. Res. Announc. Am. Math. Soc. 3 (1997), 63–71.
  • S. Kaliman and M. Zaidenberg, Affine modifications and affine hypersurfaces with a very transitive automorphism group, Transform. Groups 4 (1999), no. 1, 53–95.
  • T. Kambayashi, Automorphism group of a polynomial ring and algebraic group action on an affine space, J. Algebra 60 (1979), no. 2, 439–451.
  • T. Kambayashi and P. Russell, On linearizing algebraic torus actions, J. Pure Appl. Algebra 23 (1982), no. 3, 243–250.
  • G. Kempf, F. Knudsen, D. Mumford, and B. Saint-Donat, Toroidal embeddings. I, Lecture Notes in Math., 339, Springer-Verlag, Berlin–New York, 1973.
  • M. Koras and P. Russell, Contractible threefolds and $\mathbb{C}^{*}$-actions on $\mathbb{C}^{3}$, J. Algebraic Geom. 6 (1997), no. 4, 671–695.
  • M. Kumar and P. Murthy, Curves with negative self-intersection on rational surfaces, J. Math. Kyoto Univ. 22 (1982/83), no. 4, 767–777.
  • C. Petitjean, Cyclic cover of affine article $\mathbb{T}$-varieties, J. Pure Appl. Algebra 219 (2015), no. 9, 4265–4277.
  • C. Petitjean, Actions hyperboliques du groupe multiplicatif sur des variétés affines: espaces exotiques et structures locales, thesis, 2015.
  • H. Sumihiro, Equivariant completion, J. Math. Kyoto Univ. 14 (1974), 1–28.
  • M. Thaddeus, Geometric invariant theory and flips, J. Amer. Math. Soc. 9 (1996), no. 3, 691–723.
  • M. Zaidenberg, Lectures on exotic algebraic structures on affine spaces.. \printaddresses