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arXiv · 2309.07584

Transcendental Okounkov bodies

Tamás Darvas·Rémi Reboulet·David Witt Nyström·Mingchen Xia·Kewei Zhang
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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.

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Tamás Darvas, Rémi Reboulet, David Witt Nyström, Mingchen Xia, Kewei Zhang. 2026-01-05. Transcendental Okounkov bodies. https://arxiv.org/abs/2309.07584

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