Polynomial bounds for abelian groups of automorphisms
Catanese, Fabrizio ; Schneider, Michael
Compositio Mathematica, Tome 99 (1995), p. 1-15 / Harvested from Numdam
Publié le : 1995-01-01
@article{CM_1995__97_1-2_1_0,
     author = {Catanese, Fabrizio and Schneider, Michael},
     title = {Polynomial bounds for abelian groups of automorphisms},
     journal = {Compositio Mathematica},
     volume = {99},
     year = {1995},
     pages = {1-15},
     mrnumber = {1355114},
     zbl = {0858.14008},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CM_1995__97_1-2_1_0}
}
Catanese, Fabrizio; Schneider, Michael. Polynomial bounds for abelian groups of automorphisms. Compositio Mathematica, Tome 99 (1995) pp. 1-15. http://gdmltest.u-ga.fr/item/CM_1995__97_1-2_1_0/

[An50] Andreotti, A.: Sopra le superficie che posseggono trasformazioni birazionali in se. Rend. Mat. e Appl. 9 (1950) 255-279. | MR 49601 | Zbl 0041.08502

[BP83] Barth, W., Peters, C.: Automorphisms of Enriques surfaces. Invent. Math. 73 (1983) 383-411. | MR 718937 | Zbl 0518.14023

[Bo73] Bombieri, E.: Canonical models of surfaces of general type. Publ. Math. Inst. Hautes Etud. Sci. 42 (1973) 171-219. | Numdam | MR 318163 | Zbl 0259.14005

[CS92] Catanese, F., Schneider, M.: Bounds for stable bundles and degrees of Weierstraß schemes. Math. Ann. 293 (1992) 579-594. | MR 1176022 | Zbl 0782.14016

[Co91] Corti, A.: Polynomial bounds for the number of automorphisms of a surface of general type. Ann. Sci. Ecole Norm. Sup. 24 (1991) 113-137. | Numdam | MR 1088272 | Zbl 0758.14026

[De93] Demailly, J.P.: A numerical criterion for very ample line bundles. J. Differential Geometry 37 (1993) 323-374. | MR 1205448 | Zbl 0783.32013

[Fu78] Fujita, T.: On Kähler fibre spaces over curves. J. Math. Soc. Japan 30 (1978) 779-794. | MR 513085 | Zbl 0393.14006

[HS82] Howard, A., Sommese, A.: On the orders of the automorphism groups of certain projective manifolds. In Manifolds and Lie Groups, Progr. in Math. 14, Birkhäuser 1982, 145-158. | MR 642855 | Zbl 0483.32016

[HS90] Huckleberry, A., Sauer, M.: On the order of the automorphism group of a surface of general type. Math. Z. 205 (1990) 321-329. | MR 1076138 | Zbl 0718.32022

[Hu93] Hurwitz, A.: Über algebraische Gebilde mit eindeutigen Transformationen in sich. Math. Ann. 41 (1893) 403-442. | JFM 24.0380.02 | MR 1510753

[Ji95] Jin Xing Cai: Abelian automorphism groups of threefolds of general type. Preprint 1995. | MR 1358685

[Ka82] Kawamata, Y.: Kodaira dimension of algebraic fibre spaces over curves. Invent. Math. 66 (1982) 57-71. | MR 652646 | Zbl 0461.14004

[Ko93] Kollár, J.: Effective base point freeness. Math. Ann. 296 (1993) 595-605. | MR 1233485 | Zbl 0818.14002

[Kov] Kovacs, S.: Smooth families over rational and elliptic curves. Preprint. | MR 1374712

[Ma63] Matsumura, H.: On algebraic groups of birational transformations. Atti Accad. Naz. dei Lincei 34 (1963) 151-155. | MR 159825 | Zbl 0134.16601

[Mi] Migliorini, L.: A smooth family of minimal surfaces of general type over a curve of genus at most one is trivial. To appear in J. Alg. Geom. | MR 1311355 | Zbl 0834.14021

[Na87] Nakajima, S.: On abelian automorphism groups of algebraic curves. J. London Math. Soc. 36 (1987) 23-32. | MR 897671 | Zbl 0589.14033

[PS97] Picard, E., Simart, G: Théorie des fonctions algébriques de deux variables indépendantes. Paris, Gauthier-Villars 1897. | JFM 28.0327.01

[Ro56] Rosenlicht, M.: Some basic theorems on algebraic groups. Amer. J. Math. 78 (1956) 401-433. | MR 82183 | Zbl 0073.37601

[Sz95] Szabó, E.: Bounding automorphism groups. Preprint 1995. | MR 1380456 | Zbl 0845.14009

[Vi82] Viehweg, E.: Die Additivität der Kodaira Dimension für projektive Faserräume über Varietäten des allgemeinen Typs. J. Reine Angew. Math. 330 (1982) 132-142. | MR 641815 | Zbl 0466.14009

[Wi81] Wilson, P.: On complex algebraic varieties of general type. Symposia Math. 24 (1981) 65-73. | MR 619240 | Zbl 0462.14010

[Wi87] Wilson, P.: Towards birational classification of algebraic varieties. Bull. London Math. Soc. 19 (1987) 1-48. | MR 865038 | Zbl 0612.14033

[Xi90] Xiao Gang: On abelian automorphism groups of a surface of general type. Invent. Math. 102 (1990) 619-631. | MR 1074488 | Zbl 0739.14024

[Xi93] Xiao Gang: Bound of automorphisms of surfaces of general type I. Ann. of Math. 139 (1994) 51-77. | MR 1259364 | Zbl 0811.14011

[Xi] Xiao Gang: Bound of automorphisms of surfaces of general type II. To appear in J. Alg. Geom. | MR 1339845 | Zbl 0841.14011

[Xi95] Xiao Gang: Linear bound for abelian automorphisms of varieties of general type. Preprint 1995. | MR 1401701 | Zbl 0870.14006