Speaker
Yoshinori Hashimoto, Osaka Metropolitan University
Abstract
A foundational theorem in Kähler geometry states that a Kähler-Einstein metric exists on a Fano manifold (with discrete automorphisms) if and only if it is uniformly Ding stable. When Kähler-Einstein metrics do not exist, we can seek coupled Kähler-Einstein metrics, introduced by Hultgren and Witt Nyström, defined in terms of decompositions of the anticanonical bundle. The main result of this talk is the equivalence between the coupled uniform Ding stability (as appropriately defined) and the existence of coupled Kähler-Einstein metrics, following the strategy for Kähler-Einstein metrics due to Berman-Boucksom-Jonsson. This is a joint work with Kento Fujita.