Characterizing volume via cone duality

2015/02/23 by Jian Xiao, Xiao, Jian · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1502.06450

openalex publication_date 2015/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Kähler manifolds. In particular, for numerical equivalence classes of curves over projective varieties, it is closely related to the mobility functional.

Cited by

• Positivity functions for curves on algebraic varieties

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