Transcendental Okounkov bodies
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
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| _version_ | 1866917181144432640 |
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| author | Darvas, Tamás Reboulet, Rémi Nyström, David Witt Xia, Mingchen Zhang, Kewei |
| author_facet | Darvas, Tamás Reboulet, Rémi Nyström, David Witt Xia, Mingchen Zhang, Kewei |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_07584 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Transcendental Okounkov bodies Darvas, Tamás Reboulet, Rémi Nyström, David Witt Xia, Mingchen Zhang, Kewei Differential Geometry Algebraic Geometry Complex Variables 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. |
| title | Transcendental Okounkov bodies |
| topic | Differential Geometry Algebraic Geometry Complex Variables |
| url | https://arxiv.org/abs/2309.07584 |