A simple proof for the existence of Zariski decompositions on surfaces
Algebraic Geometry
2007-12-11 v1
Abstract
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.
Keywords
Cite
@article{arxiv.0712.1576,
title = {A simple proof for the existence of Zariski decompositions on surfaces},
author = {Thomas Bauer},
journal= {arXiv preprint arXiv:0712.1576},
year = {2007}
}