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arXiv · 1502.06450

Characterizing volume via cone duality

Jian Xiao
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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.

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Jian Xiao. 2015-02-23. Characterizing volume via cone duality. https://arxiv.org/abs/1502.06450

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