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PreprintarXiv licencearXiv

A solution to the Yau-Tian-Donaldson Conjecture through Special Fujita Approximations

  • Antonio Trusiani1
  1. 1Università di Roma Tor Vergata , Via della Ricerca Scientifica 1 , 00133 , Roma , Italy
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Abstract

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 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 Aut∘(X,L)-uniformly K-stable. This extends the known Yau-Tian-Donaldson correspondence for smooth Fano varieties.

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Cite

BibTeXRIS
BibTeX
@misc{trusiani2026solution,
  title = {{A solution to the Yau-Tian-Donaldson Conjecture through Special Fujita Approximations}},
  author = {Antonio Trusiani},
  howpublished = {arXiv},
  year = {2026},
  month = may,
  doi = {10.48550/arxiv.2605.30063},
  eprint = {2605.30063},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.30063},
}
RIS
TY  - UNPB
TI  - A solution to the Yau-Tian-Donaldson Conjecture through Special Fujita Approximations
AU  - Antonio Trusiani
PY  - 2026
DA  - 2026/05/28
PB  - arXiv
DO  - 10.48550/arxiv.2605.30063
UR  - https://arxiv.org/abs/2605.30063
AB  - 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 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 Aut^∘(X,L)-uniformly K-stable. This extends the known Yau-Tian-Donaldson correspondence for smooth Fano varieties.
SN  - 2331-8422
ER  -