2010/05/10 by Shin-ichi Matsumura, Matsumura, Shin-ichi · 2 citations
Mathematics · #14C20 #32J25 #32J27 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics #math.AG #math.CV #msc:14C20 #msc:32J25 #msc:32J27
paper · pdf · doi:10.48550/arxiv.1005.1503
24 pages, to appear in Amer. J. Math, v2: completely revised
arxiv created 2013/01/16 · arxiv updated 2013/01/17
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.