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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Classification of quadruple Galois canonical covers I


Authors: Francisco Javier Gallego and Bangere P. Purnaprajna
Journal: Trans. Amer. Math. Soc. 360 (2008), 5489-5507
MSC (2000): Primary 14J10, 14J26, 14J29
Published electronically: May 28, 2008
MathSciNet review: 2415082
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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

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04587-X
PII: S 0002-9947(08)04587-X
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
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.