Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Trusiani, Antonio
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214615221