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On the Bicanonical Morphism of quadruple Galois canonical covers

Gallego Rodrigo, Francisco Javier and Purnaprajna, Bangere P. (2011) On the Bicanonical Morphism of quadruple Galois canonical covers. Transactions of the American Mathematical Society, 363 (8). pp. 4401-4420. ISSN 1088-6850

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Abstract

I In this article we study the bicanonical map ϕ2 of quadruple Galois canonical covers X of surfaces of minimal degree. We show that ϕ2 has diverse behavior and exhibits most of the complexities that are possible for a bicanonical map of surfaces of general type, depending on the type of X.
There are cases in which ϕ2 is an embedding, and if it so happens, ϕ2 embeds X as a projectively normal variety, and there are cases in which ϕ2 is not an embedding. If the latter, ϕ2 is finite of degree 1, 2 or 4. We also study the
canonical ring of X, proving that it is generated in degree less than or equal to 3 and finding the number of generators in each degree. For generators of degree 2 we find a nice general formula which holds for canonical covers of arbitrary degrees. We show that this formula depends only on the geometric and the arithmetic genus of X.


Item Type:Article
Additional Information:

First published in Transactions of the American Mathematical Society in Volume 363, Number 8, August 2011, published by the American Mathematical Society

Uncontrolled Keywords:Surfaces of general type, Bicanonical map, Quadruple Galois canonical covers, Canonical ring, Surfaces of minimal degree
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:12608
Deposited On:25 Apr 2011 20:43
Last Modified:06 Feb 2014 09:28

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