Characterizing volume via cone duality - Archive ouverte HAL
Article Dans Une Revue Mathematische Annalen Année : 2017

Characterizing volume via cone duality

Jian Xiao
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Résumé

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.

Dates et versions

hal-01684158 , version 1 (15-01-2018)

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Jian Xiao. Characterizing volume via cone duality. Mathematische Annalen, 2017, 369 (3-4), pp.1527 - 1555. ⟨10.1007/s00208-016-1501-3⟩. ⟨hal-01684158⟩
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