no. 2
Connected algebraic groups acting on algebraic surfaces
[Groupes algébriques connexes agissant sur les surfaces algébriques]
Fong, Pascal1
1 Universität Basel Departement Mathematik und Informatik Spiegelgasse 1 CH–4051 Basel (Switzerland)
Annales de l'Institut Fourier, Tome 74 (2024) no. 2, pp. 545-587.

Nous classifions les sous-groupes algébriques connexes maximaux de Bir(X), quand X est une surface

We classify the maximal connected algebraic subgroups of Bir(X), when X is a surface.

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DOI : 10.5802/aif.3595
Classification : 14E05, 14E07, 14L30, 14J50, 14H60
Keywords: Algebraic groups, birational automorphisms, surfaces
Mot clés : groupes algébriques, automorphismes birationnels, surfaces

Fong, Pascal 1

1 Universität Basel Departement Mathematik und Informatik Spiegelgasse 1 CH–4051 Basel (Switzerland)
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Fong, Pascal. Connected algebraic groups acting on algebraic surfaces. Annales de l'Institut Fourier, Tome 74 (2024) no. 2, pp. 545-587. doi : 10.5802/aif.3595. https://aif.centre-mersenne.org/articles/10.5802/aif.3595/

[1] Atiyah, Michael F. Vector bundles over an elliptic curve, Proc. Lond. Math. Soc., Volume 7 (1957), pp. 414-452 | DOI | MR | Zbl

[2] Beauville, Arnaud Complex algebraic surfaces, London Mathematical Society Student Texts, 34, Cambridge University Press, 1996, x+132 pages (translated from the 1978 French original by R. Barlow, with assistance from N. I. Shepherd-Barron and M. Reid) | DOI | MR

[3] Bennett, Curtis; Miranda, Rick The automorphism groups of the hyperelliptic surfaces, Rocky Mt. J. Math., Volume 20 (1990) no. 1, pp. 31-37 | DOI | MR | Zbl

[4] Blanc, Jérémy Sous-groupes algébriques du groupe de Cremona, Transform. Groups, Volume 14 (2009) no. 2, pp. 249-285 | DOI | MR | Zbl

[5] Blanc, Jérémy; Fanelli, Andrea; Terpereau, Ronan Connected algebraic groups acting on 3-dimensional Mori fibrations (2019) | arXiv

[6] Brion, Michel Algebraic group actions on normal varieties, Trans. Mosc. Math. Soc., Volume 78 (2017), pp. 85-107 | DOI | MR | Zbl

[7] Brion, Michel Notes on automorphism groups of projective varieties, 2019 (text available on http://www-fourier.univ-grenoble-alpes.fr/~mbrion/autos_final.pdf)

[8] Brion, Michel; Samuel, Preena; Uma, Vikraman Lectures on the structure of algebraic groups and geometric applications, CMI Lecture Series in Mathematics, 1, Hindustan Book Agency; Chennai Mathematical Institute, 2013, viii+120 pages | DOI | MR

[9] Enriques, Federigo Sui gruppi continui di trasformazioni cremoniane nel piano, Rom. Acc. L. Rend. (5), Volume 2 (1893) no. 1, pp. 468-473 | Zbl

[10] Fujino, Osamu Iitaka conjecture. An introduction, SpringerBriefs in Mathematics, Springer, 2020, 128 pages | DOI | MR

[11] Grothendieck, Alexander Éléments de géométrie algébrique. IV. Étude locale des schémas et des morphismes de schémas IV, Publ. Math., Inst. Hautes Étud. Sci. (1967) no. 32, p. 361 | Numdam | MR | Zbl

[12] Hartshorne, Robin Algebraic geometry, Graduate Texts in Mathematics, 52, Springer, 1977, xvi+496 pages | DOI | MR

[13] Jacobson, Nathan Basic algebra. I, WH Freeman & Co, 1985, xviii+499 pages | MR

[14] Kraft, Hanspeter Regularization of Rational Group Actions (2018) | arXiv

[15] Laurent, Bruno Almost homogeneous varieties of Albanese codimension one (2020) | arXiv

[16] Lipman, Joseph Desingularization of two-dimensional schemes, Ann. Math., Volume 107 (1978) no. 1, pp. 151-207 | DOI | MR | Zbl

[17] Lonjou, Anne; Urech, Christian Actions of Cremona groups on CAT(0) cube complexes (2021) | arXiv

[18] Loray, Frank; Marín Pérez, David Projective structures and projective bundles over compact Riemann surfaces, Differential equations and singularities (Astérisque), Volume 323, Société Mathématique de France, 2009, pp. 223-252 | Numdam | MR | Zbl

[19] Maruyama, Masaki On classification of ruled surfaces, Lectures in Mathematics, Department of Mathematics, Kyoto University, 3, Kinokuniya Book-Store Co., 1970, iv+75 pages | MR

[20] Maruyama, Masaki On automorphism groups of ruled surfaces, J. Math. Kyoto Univ., Volume 11 (1971), pp. 89-112 | DOI | MR | Zbl

[21] Matsumura, Hideyuki; Oort, Frans Representability of group functors, and automorphisms of algebraic schemes, Invent. Math., Volume 4 (1967), pp. 1-25 | DOI | MR | Zbl

[22] Mumford, David Abelian varieties, Tata Institute of Fundamental Research Studies in Mathematics, 5, Hindustan Book Agency, 2008, xii+263 pages with appendices by C. P. Ramanujam and Yuri Manin, corrected reprint of the second (1974) edition | MR

[23] Robayo, Maria Fernanda; Zimmermann, Susanna Infinite algebraic subgroups of the real Cremona group, Osaka J. Math., Volume 55 (2018) no. 4, pp. 681-712 | MR | Zbl

[24] Rosenlicht, Maxwell Some basic theorems on algebraic groups, Am. J. Math., Volume 78 (1956), pp. 401-443 | DOI | MR

[25] Serre, Jean-Pierre Groupes algébriques et corps de classes, Publications de l’Institut de Mathématique de l’Université de Nancago, 7, Hermann, 1984, 207 pages (Actualités Scientifiques et Industrielles, 1264) | MR

[26] The Stacks Project Authors The Stacks project, https://stacks.math.columbia.edu, 2021

[27] Weil, André On algebraic groups of transformations, Am. J. Math., Volume 77 (1955), pp. 355-391 | DOI | MR | Zbl

[28] Zaitsev, Dmitri Regularization of birational group operations in the sense of Weil, J. Lie Theory, Volume 5 (1995) no. 2, pp. 207-224 | MR | Zbl

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