2007/12/10 by Bauer, Thomas
#14C20 #14F05 #Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.0712.1576
In this note we give a quick and simple proof of the existence (and uniqueness) of Zariski decompositions on surfaces. While Zariski's original proof employs a rather sophisticated procedure to construct the negative part of the decomposition, the present approach is based on the idea that the positive part can be constructed from a maximality condition. It may also be useful that this approach yields a practical algorithm for the computation of the positive part.