%0 Journal Article
%T Characterizing volume via cone duality
%A Jian Xiao
%J Mathematics
%D 2015
%I arXiv
%X For divisors over smooth projective varieties, we show that the volume can be characterized by the duality between pseudo-effective cone of divisors and movable cone of curves. Inspired by this result, we give and study a natural intersection-theoretic volume functional for 1-cycles over compact K\"ahler manifolds. In particular, for numerical equivalence classes of curves over projective varieties, it is closely related to the mobility functional.
%U http://arxiv.org/abs/1502.06450v1