Convexity of the Mabuchi functional in big cohomology classes
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| author | Di Nezza, Eleonora Trapani, Stefano Trusiani, Antonio |
| author_facet | Di Nezza, Eleonora Trapani, Stefano Trusiani, Antonio |
| contents | We study the Mabuchi functional associated to a big cohomology class. We define an invariant associated to transcendental Fujita approximations, whose vanishing is related to the Yau-Tian Donaldson conjecture. Assuming vanishing (finiteness) of this invariant we establish (almost) convexity along weak geodesics. As an application, we give an explicit expression of the distance $d_p$ in the big setting for finite entropy potentials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_08984 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convexity of the Mabuchi functional in big cohomology classes Di Nezza, Eleonora Trapani, Stefano Trusiani, Antonio Differential Geometry Complex Variables 32W20, 32U05, 32Q15, 35A23 We study the Mabuchi functional associated to a big cohomology class. We define an invariant associated to transcendental Fujita approximations, whose vanishing is related to the Yau-Tian Donaldson conjecture. Assuming vanishing (finiteness) of this invariant we establish (almost) convexity along weak geodesics. As an application, we give an explicit expression of the distance $d_p$ in the big setting for finite entropy potentials. |
| title | Convexity of the Mabuchi functional in big cohomology classes |
| topic | Differential Geometry Complex Variables 32W20, 32U05, 32Q15, 35A23 |
| url | https://arxiv.org/abs/2410.08984 |