Characterizing volume via cone duality
Algebraic Geometry
2015-02-24 v1 Complex Variables
Abstract
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.
Cite
@article{arxiv.1502.06450,
title = {Characterizing volume via cone duality},
author = {Jian Xiao},
journal= {arXiv preprint arXiv:1502.06450},
year = {2015}
}