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arXiv · 1005.1503

Restricted volumes and divisorial Zariski decompositions

Shin-ichi Matsumura
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Abstract

We give a relation between the existence of a Zariski decomposition and the behavior of the restricted volume of a big divisor on a smooth (complex) projective variety. Moreover, we give an analytic description of the restricted volume in the line of Boucksom's work. It enables us to define the restricted volume of a transcendental class on a compact Kähler manifold in natural way. The relation can be extended to a transcendental class.

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Shin-ichi Matsumura. 2013-01-16. Restricted volumes and divisorial Zariski decompositions. https://arxiv.org/abs/1005.1503

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