In this talk, we will introduce the notion of complements and show the connection of lc places of complements with special valuations (cf. Theorem A.2 of [BLX19], Section 4 of [Xu])

 

Ref.

[BLX19] H. Blum, Y. Liu, and C. Xu, Openness of K-semistability for Fano varieties, arXiv:1907.02408 (2019).

[Xu] C. Xu, K-stability of Fano varieties: an algebro-geometric Approach