Zariski decomposition: a new (old) chapter of linear algebra
Algebraic Geometry
2011-06-27 v2 History and Overview
Abstract
In a 1962 paper, Zariski introduced the decomposition theory that now bears his name. Although it arose in the context of algebraic geometry and deals with the configuration of curves on an algebraic surface, we have recently observed that the essential concept is purely within the realm of linear algebra. In this paper, we formulate Zariski decomposition as a theorem in linear algebra and present a linear algebraic proof. We also sketch the geometric context in which Zariski first introduced his decomposition.
Keywords
Cite
@article{arxiv.0911.4500,
title = {Zariski decomposition: a new (old) chapter of linear algebra},
author = {Thomas Bauer and Mirel Caibar and Gary Kennedy},
journal= {arXiv preprint arXiv:0911.4500},
year = {2011}
}
Comments
20 pages, 5 figures; many small changes have been made to the previous version; the paper will appear in the American Math. Monthly