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 K̈ahler manifold in a natural way. The relation can be extended to a transcendental class.
|Number of pages||26|
|Journal||American Journal of Mathematics|
|Publication status||Published - 2013 Jun 1|
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