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
Official URL: http://www.ams.org/home/page
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.
|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|
|Deposited On:||25 Apr 2011 20:43|
|Last Modified:||06 Feb 2014 09:28|
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