Characterizations of Fano type varieties and projective spaces via absolute complexity

In this paper, we obtain several characterizations of varieties of Fano type and projective spaces via absolute complexity. Also, we show that if the absolute complexity of a given pair \((X,\Delta )\) $(X,\mathrm{\Delta })$ is negative, then the pair \((X,\Delta )\) $(X,\mathrm{\Delta })$ does not admit any \(-(K_X+\Delta )\) $-(K_X+\mathrm{\Delta })$ -minimal models.