%0 Journal Article
%A Gallego Rodrigo, Francisco Javier
%A Purnaprajna, Bangere P.
%T On the Bicanonical Morphism of quadruple Galois canonical covers
%D 2011
%@ 1088-6850
%U https://hdl.handle.net/20.500.14352/41932
%X 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 thecanonical 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.
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