Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Construction of covers in positive characteristic via degeneration


Author: Irene I. Bouw
Journal: Proc. Amer. Math. Soc. 137 (2009), 3169-3176
MSC (2000): Primary 14H30, 14H10
DOI: https://doi.org/10.1090/S0002-9939-09-10013-8
Published electronically: June 3, 2009
MathSciNet review: 2515387
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we construct examples of covers of the projective line in positive characteristic such that every degeneration is inseparable. The result illustrates that it is not possible to construct all covers of the generic $ r$-pointed curve of genus zero inductively from covers with a smaller number of branch points.


References [Enhancements On Off] (What's this?)

  • 1. I. I. Bouw.
    The $ p$-rank of curves and covers of curves.
    In: Courbes semi-stables et groupes fondamental en géométrie algébrique (Luminy, 1998), Progress in Math. 187: 267-277, Birkhäuser, 2000. MR 1768105 (2001j:14042)
  • 2. I. I. Bouw.
    The $ p$-rank of ramified covers of curves.
    Compositio Math., 126:295-322, 2001. MR 1834740 (2002e:14045)
  • 3. A. Elkin.
    The rank of the Cartier operator on cyclic covers of the projective line.
    Preprint, arXiv:0708.0431.
  • 4. D. Harbater and K. Stevenson.
    Patching and thickening problems.
    J. Algebra, 212:272-304, 1999. MR 1670658 (2000b:14004)
  • 5. B. Osserman.
    Linear series and existence of branched covers.
    Compositio Math., 144:89-106, 2008. MR 2388557 (2009b:14056)
  • 6. M. Romagny and S. Wewers.
    Hurwitz spaces.
    In: Groupes de Galois arithmétiques et différentiels. Séminaires et Congrès 13:313-341, Soc. Math. France, Paris, 2006. MR 2316356 (2008e:14040)
  • 7. S. Wewers.
    Deformation of tame admissible covers of curves.
    In: Aspects of Galois theory (Gainesville, FL, 1996), London Math. Soc. Lecture Note Ser. 256:239-282, Cambridge Univ. Press, 1999. MR 1708609 (2001b:14048)
  • 8. S. Wewers and I. I. Bouw.
    Alternating groups as monodromy groups in positive characteristic.
    Pacific J. Math. 222:185-200, 2005. MR 2200250 (2006k:14050)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 14H30, 14H10

Retrieve articles in all journals with MSC (2000): 14H30, 14H10


Additional Information

Irene I. Bouw
Affiliation: Institut für Reine Mathematik, Helmholtzstraße 18, D-89069 Ulm, Germany
Email: irene.bouw@uni-ulm.de

DOI: https://doi.org/10.1090/S0002-9939-09-10013-8
Received by editor(s): September 13, 2007
Published electronically: June 3, 2009
Communicated by: Ted Chinburg
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society