# Characterizing volume via cone duality

@article{Xiao2015CharacterizingVV, title={Characterizing volume via cone duality}, author={Jian Xiao}, journal={Mathematische Annalen}, year={2015}, volume={369}, pages={1527-1555} }

For divisors over smooth projective varieties, we show that the volume can be characterized by the duality between the pseudo-effective cone of divisors and the movable cone of curves. Inspired by this result, we define and study a natural intersection-theoretic volume functional for 1-cycles over compact Kähler manifolds. In particular, for numerical equivalence classes of curves over projective varieties, it is closely related to the mobility functional studied by Lehmann.

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