Bounded Complements for $\epsilon-lc$ generalized Fano Pairs

We show the existence of strong ($\epsilon,n,\Gamma$)-complements for $\epsilon-lc$ generalized Fano pairs with coefficients of boundaries in a fixed DCC set, for any non-negative real number $\epsilon$, given a certain ACC (ascending chain condition) for generalized \epsilon-log canonical threshold. This is a generalization combining Filipazzi-Moraga's result in 2018 and Han-Liu-Shokurov's result in 2019, which are based on Birkar's construction in 2016. This is a joint work with Y. Gongyo and Y. Nakamura.