We prove the following result:if aℚ-Fano variety is uniformly K-stable,then it admits a Kähler–Einstein metric.This proves the uniform version of Yau–Tian–Donaldson conjecture for all(singular)Fano varieties w...We prove the following result:if aℚ-Fano variety is uniformly K-stable,then it admits a Kähler–Einstein metric.This proves the uniform version of Yau–Tian–Donaldson conjecture for all(singular)Fano varieties with discrete automorphism groups.We achieve this by modifying Berman–Boucksom–Jonsson’s strategy in the smooth case with appropriate perturbative arguments.This perturbation approach depends on the valuative criterion and non-Archimedean estimates,and is motivated by our previous paper.展开更多
基金supported by NSF(Grant No.DMS-1810867)research fellowship.G.Tian is partially supported by NSF(Grant No.DMS-1607091)and NSFC(Grant No.11331001)partially supported by NSFC(Grant No.11501501).
文摘We prove the following result:if aℚ-Fano variety is uniformly K-stable,then it admits a Kähler–Einstein metric.This proves the uniform version of Yau–Tian–Donaldson conjecture for all(singular)Fano varieties with discrete automorphism groups.We achieve this by modifying Berman–Boucksom–Jonsson’s strategy in the smooth case with appropriate perturbative arguments.This perturbation approach depends on the valuative criterion and non-Archimedean estimates,and is motivated by our previous paper.
