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Classification of quadruple Galois canonical covers I

Gallego Rodrigo, Francisco Javier and Purnaprajna, Bangere P. (2008) Classification of quadruple Galois canonical covers I. Transactions of the American Mathematical Society, 360 (10). pp. 5489-5507. ISSN 1088-6850

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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.


Item Type:Article
Additional Information:

First published in Transactions of the American Mathematical Society in Volume 360, Number 10, October 2008, published by the American Mathematical Society

Uncontrolled Keywords:Calabi-Yau threefolds, General type, Algebraic-surfaces, C1(2)
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:12606
Deposited On:25 Apr 2011 20:54
Last Modified:06 Feb 2014 09:28

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