Transcendental Okounkov bodies

2023/09/14 by Tamás Darvas, Darvas, Tamás, Rémi Reboulet +7 · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2309.07584

openalex publication_date 2023/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the volume of transcendental big (1,1)-classes on compact Kähler manifolds can be realized by convex bodies, thus answering questions of Lazarsfeld-Mustaţă and Deng. In our approach we use an approximation process by partial Okounkov bodies together with properties of the restricted volume, and we study the extension of Kähler currents, as well as the bimeromorphic behavior of currents with analytic singularities. We also establish a connection between transcendental Okounkov bodies and toric degenerations.

Cited by

• On the extension of Kähler currents on compact complex manifolds

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