A solution to the Yau-Tian-Donaldson Conjecture through Special Fujita Approximations
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arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910270274666496 |
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| author | Trusiani, Antonio |
| author_facet | Trusiani, Antonio |
| contents | We show that any big line bundle on a smooth projective variety admits a special Fujita approximation: the volume and the first Riemann-Roch coefficient are both approximated by those of ample $\mathbb{Q}$-line bundles on higher models. Exploiting previous works by Boucksom, Jonsson and Li, we solve the Boucksom-Jonsson Regularization Conjecture on the Non-Archimedean entropy functional. As a main consequence, we obtain a solution to the (uniform version of the) Yau-Tian-Donaldson Conjecture: a polarized smooth projective variety $(X,L)$ admits a cscK metric if and only if it is $\mathrm{Aut}^\circ(X,L)$-uniformly $K$-stable. This extends the known Yau-Tian-Donaldson correspondence for smooth Fano varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_30063 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A solution to the Yau-Tian-Donaldson Conjecture through Special Fujita Approximations Trusiani, Antonio Algebraic Geometry Complex Variables Differential Geometry We show that any big line bundle on a smooth projective variety admits a special Fujita approximation: the volume and the first Riemann-Roch coefficient are both approximated by those of ample $\mathbb{Q}$-line bundles on higher models. Exploiting previous works by Boucksom, Jonsson and Li, we solve the Boucksom-Jonsson Regularization Conjecture on the Non-Archimedean entropy functional. As a main consequence, we obtain a solution to the (uniform version of the) Yau-Tian-Donaldson Conjecture: a polarized smooth projective variety $(X,L)$ admits a cscK metric if and only if it is $\mathrm{Aut}^\circ(X,L)$-uniformly $K$-stable. This extends the known Yau-Tian-Donaldson correspondence for smooth Fano varieties. |
| title | A solution to the Yau-Tian-Donaldson Conjecture through Special Fujita Approximations |
| topic | Algebraic Geometry Complex Variables Differential Geometry |
| url | https://arxiv.org/abs/2605.30063 |