Moment maps and equivariant volumes
  The study of the volume of big line bundles on a complex projective manifold M has been one of the main veins in the recent interest in the asymptotic properties of linear series. In this article, we consider an equivariant version of this problem, in the presence of a linear action of a reductive group on M. The results in this paper extend and improve those in our previous unpublished work math.AG/0412433. 
Alberto Della Vedova, Roberto Paoletti