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PreprintarXiv licencearXiv

On the transcendental Yau-Tian-Donaldson Conjecture

  • Antonio Trusiani
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Abstract

We prove the (uniform) Yau-Tian-Donaldson Conjecture for transcendental Kähler classes in the case of trivial automorphisms. Indeed, we show the existence of Special Kähler Fujita Approximations of big cohomology classes associated to big test configurations, establishing the equivalence between the uniform K-stability and the strengthened version for models. More generally, we show that any big cohomology class on a compact Kähler manifold admits such Special Kähler Fujita Approximations: the volume and the analogue of the Riemann-Roch coefficient of the big class are both approximated by those of Kähler classes on higher compactifications.

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Cite

BibTeXRIS
BibTeX
@misc{trusiani2026transcendental,
  title = {{On the transcendental Yau-Tian-Donaldson Conjecture}},
  author = {Antonio Trusiani},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.31089},
  eprint = {2609.31089},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.31089},
}
RIS
TY  - UNPB
TI  - On the transcendental Yau-Tian-Donaldson Conjecture
AU  - Antonio Trusiani
PY  - 2026
DA  - 2026/10/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.31089
UR  - https://arxiv.org/abs/2609.31089
AB  - We prove the (uniform) Yau-Tian-Donaldson Conjecture for transcendental Kähler classes in the case of trivial automorphisms. Indeed, we show the existence of Special Kähler Fujita Approximations of big cohomology classes associated to big test configurations, establishing the equivalence between the uniform K-stability and the strengthened version for models. More generally, we show that any big cohomology class on a compact Kähler manifold admits such Special Kähler Fujita Approximations: the volume and the analogue of the Riemann-Roch coefficient of the big class are both approximated by those of Kähler classes on higher compactifications.
ER  -