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Izv. RAN. Ser. Mat., 2009, Volume 73, Issue 1, Pages 121–156 (Mi izv2723)  

This article is cited in 2 scientific papers (total in 2 papers)

Automorphisms of Galois coverings of generic $m$-canonical projections

Vik. S. Kulikova, V. M. Kharlamovb

a Steklov Mathematical Institute, Russian Academy of Sciences
b University Louis Pasteur

Abstract: 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, Galois extensions, automorphism group of a projective variety.

DOI: https://doi.org/10.4213/im2723

Full text: PDF file (756 kB)
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English version:
Izvestiya: Mathematics, 2009, 73:1, 121–150

Bibliographic databases:

Document Type: Article
UDC: 512.7
MSC: 14E20, 14F35, 14J15, 14J29, 14P25, 32G05, 57R17, 57R50
Received: 04.09.2007

Citation: Vik. S. Kulikov, V. M. Kharlamov, “Automorphisms of Galois coverings of generic $m$-canonical projections”, Izv. RAN. Ser. Mat., 73:1 (2009), 121–156; Izv. Math., 73:1 (2009), 121–150

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Vik. S. Kulikov, E. I. Shustin, “On $G$-Rigid Surfaces”, Proc. Steklov Inst. Math., 298 (2017), 133–151  mathnet  crossref  crossref  isi  elib
    2. Artal Bartolo E., Ignacio Cogolludo-Agustin J., “Some Open Questions on Arithmetic Zariski Pairs”, Singularities in Geometry, Topology, Foliations and Dynamics: a Celebration of the 60Th Birthday of Jose Seade, Trends in Mathematics, eds. CisnerosMolina J., Le D., Oka M., Snoussi J., Springer International Publishing Ag, 2017, 31–54  crossref  mathscinet  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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