In this paper, we develop a theory of diminished multiplier ideal on singular varieties which notion was introduced by Lehmann, and we prove a result regarding the termination of certain class of flips with scaling of an ample divisor with bounded index if κσ(KX+Δ)≥ X-1 holds using the theory of diminished multiplier ideal.
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Donghyeon Kim (2024) studied this question.
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