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Characterizing volume via cone duality
Published 23 Feb 2015 in math.AG and math.CV | (1502.06450v1)
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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