Geodesic
Automorphisms of Galois coverings of generic $m$-canonical projections
Izvestiya. Mathematics , Tome 73 (2009) no. 1, pp. 121-150.

Voir la notice de l'article provenant de la source Math-Net.Ru

We investigate the automorphism groups of Galois coverings induced by pluricanonical generic coverings of projective spaces. In dimensions one and two, it is shown that such coverings yield sequences of examples where specific actions of the symmetric group $S_d$ on curves and surfaces cannot be deformed together with the action of $S_d$ into manifolds whose automorphism group does not coincide with $S_d$. As an application, we give new examples of complex and real $G$-varieties which are diffeomorphic but not deformation equivalent.
Keywords: generic coverings of projective lines and planes, Galois group of a covering, automorphism group of a projective variety.
Mots-clés : Galois extensions 
@article{IM2_2009_73_1_a6,
     author = {Vik. S. Kulikov and V. M. Kharlamov},
     title = {Automorphisms of {Galois} coverings of generic $m$-canonical projections},
     journal = {Izvestiya. Mathematics },
     pages = {121--150},
     publisher = {mathdoc},
     volume = {73},
     number = {1},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2009_73_1_a6/}
}
TY  - JOUR
AU  - Vik. S. Kulikov
AU  - V. M. Kharlamov
TI  - Automorphisms of Galois coverings of generic $m$-canonical projections
JO  - Izvestiya. Mathematics 
PY  - 2009
SP  - 121
EP  - 150
VL  - 73
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2009_73_1_a6/
LA  - en
ID  - IM2_2009_73_1_a6
ER  - 
%0 Journal Article
%A Vik. S. Kulikov
%A V. M. Kharlamov
%T Automorphisms of Galois coverings of generic $m$-canonical projections
%J Izvestiya. Mathematics 
%D 2009
%P 121-150
%V 73
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2009_73_1_a6/
%G en
%F IM2_2009_73_1_a6
Vik. S. Kulikov; V. M. Kharlamov. Automorphisms of Galois coverings of generic $m$-canonical projections. Izvestiya. Mathematics , Tome 73 (2009) no. 1, pp. 121-150. http://geodesic.mathdoc.fr/item/IM2_2009_73_1_a6/

[1] H. Weyl, Philosophy of mathematics and natural science, Princeton Univ. Press, Princeton, NJ, 1949 | MR | Zbl

[2] V. S. Kulikov, Vik. S. Kulikov, “Generic coverings of the plane with $A$-$D$-$E$-singularities”, Izv. Math., 64:6 (2000), 1153–1195 | DOI | MR | Zbl

[3] Vik. S. Kulikov, V. M. Kharlamov, “Surfaces with ${\rm DIF}\neq{\rm DEF}$ real structures”, Izv. Math., 70:4 (2006), 769–807 | DOI | MR | Zbl

[4] D. Gorenstein, Finite simple groups. An introduction to their classification, University Series in Mathematics, Plenum, New York–London, 1982 | MR | MR | Zbl | Zbl

[5] H. M. Farkas, I. Kra, Riemann surfaces, Grad. Texts in Math., 71, Springer-Verlag, New York–Heidelberg–Berlin, 1980 | MR | Zbl

[6] H. Cartan, “Quotient d'un espace analytique par un groupe d'automorphismes”, Algebraic geometry and topology, A symposium in honor of S. Lefschetz (Princeton, 1954), Princeton Univ. Press, Princeton, NJ, 1957, 90–102 | MR | Zbl

[7] Vik. S. Kulikov, “On Chisini's conjecture”, Izv. Math., 63:6 (1999), 1139–1170 | DOI | MR | Zbl

[8] G. Xiao, “Bound of automoprhisms of surfaces of general type. II”, J. Algebraic Geom., 4:4 (1995), 701–793 | MR | Zbl

[9] L. Dornhoff, Group representation theory. Part A: Ordinary representation theory, Pure Appl. Math., 7, Dekker, New York, 1971 | MR | Zbl

[10] Vik. S. Kulikov, “Generalized Chisini's conjecture”, Proc. Steklov Inst. Math., 241 (2003), 110–119 | MR | Zbl

[11] W. Barth, C. Peters, A. Van de Ven, Compact complex surfaces, Ergeb. Math. Grenzgeb. (3), 4, Springer-Verlag, Berlin, 1984 | MR | Zbl

[12] Yum-Tong Siu, “Global nondeformability of the complex projective space”, Prospects in complex geometry (Katata and Kyoto, 1989), Lecture Notes in Math., 1468, Springer-Verlag, Berlin, 1991, 254–280 | DOI | MR | Zbl

[13] Vik. S. Kulikov, V. M. Kharlamov, “On real structures on rigid surfaces”, Izv. Math., 66:1 (2002), 133–150 | DOI | MR | Zbl

[14] R. Hartshorne, Ample subvarieties of algebraic varieties, Lecture Notes in Math., 156, Springer-Verlag, Berlin–New York, 1970 | DOI | MR | Zbl