TRANSCENDENTAL OKOUNKOV BODIES
Journal article, 2026
We show that the volume of transcendental big (1, 1)-classes on compact Kahler manifolds can be realized by convex bodies, thus answering questions of Lazarsfeld-Mustata 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 Kahler currents, as well as the bimeromorphic behavior of currents with analytic singularities. We also establish a connection between transcendental Okounkov bodies and toric degenerations.
Author
Tamas Darvas
University of Maryland
Remi Reboulet
Inst Camille Jordan
David Witt Nyström
Chalmers, Mathematical Sciences, Algebra and geometry
University of Gothenburg
Mingchen Xia
University of Science and Technology of China
Kewei Zhang
Beijing Normal University
Journal of Differential Geometry
0022-040X (ISSN) 1945743x (eISSN)
Vol. 132 1 135-178Subject Categories (SSIF 2025)
Geometry