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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Classification of quadruple Galois canonical covers I
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by Francisco Javier Gallego and Bangere P. Purnaprajna PDF
Trans. Amer. Math. Soc. 360 (2008), 5489-5507 Request permission

Abstract:

In this article we classify quadruple Galois canonical covers of smooth surfaces of minimal degree. The classification shows that they are either non-simple cyclic covers or bi-double covers. If they are bi-double, then they are all fiber products of double covers. We construct examples to show that all the possibilities in the classification do exist. There are implications of this classification that include the existence of families with unbounded geometric genus, in sharp contrast with triple canonical covers, and families with unbounded irregularity, in sharp contrast with canonical covers of all other degrees. Together with the earlier known results on double and triple covers, a pattern emerges that motivates some general questions on the existence of higher degree canonical covers, some of which are answered in this article.
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Additional Information
  • Francisco Javier Gallego
  • Affiliation: Departamento de Álgebra, Facultad de Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain
  • Email: gallego@mat.ucm.es
  • Bangere P. Purnaprajna
  • Affiliation: Department of Mathematics, 405 Snow Hall, University of Kansas, Lawrence, Kansas 66045-2142
  • Email: purna@math.ku.edu
  • Received by editor(s): November 15, 2006
  • Published electronically: May 28, 2008
  • Additional Notes: The first author was partially supported by MCT project number BFM2000-0621. He is grateful for the hospitality of the Department of Mathematics of the University of Kansas at Lawrence.
    The second author is grateful to NSA and the GRF of the University of Kansas for supporting this research project. He is also grateful for the hospitality of the Departamento de Álgebra of the Universidad Complutense de Madrid

  • Dedicated: Dedicated to Ignacio Sols
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 360 (2008), 5489-5507
  • MSC (2000): Primary 14J10, 14J26, 14J29
  • DOI: https://doi.org/10.1090/S0002-9947-08-04587-X
  • MathSciNet review: 2415082