Zariski decomposition: a new (old) chapter of linear algebra

Details Zariski decomposition: a new (old) chapter of linear algebra Zariski decomposition: a new (old) chapter of linear algebra

2009-11-23

arxiv.org/abs/0911.4500v2

Mathematics

Algebraic Geometry

20 pages, 5 figures; many small changes have been made to the previous version; the paper will appear in the American Math. Mo

Scientific paper

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.

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