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arXiv · 0712.1576

A simple proof for the existence of Zariski decompositions on surfaces

Thomas Bauer
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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.

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Thomas Bauer. 2007-12-10. A simple proof for the existence of Zariski decompositions on surfaces. https://arxiv.org/abs/0712.1576

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