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Zariski Decomposition: A New (Old) Chapter of Linear Algebra

Thomas Bauer, Mirel Caibăr and Gary Kennedy
The American Mathematical Monthly
Vol. 119, No. 1 (January 2012), pp. 25-41
DOI: 10.4169/amer.math.monthly.119.01.025
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Page Count: 17
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Zariski Decomposition: A New (Old) Chapter of Linear
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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.

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