Characterizing volume via cone duality

Jian Xiao (1, 2)

1 IF - Institut Fourier
2 Fudan University [Shanghai]

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.

Domaines: Mathématiques [math]

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