On diminished multiplier ideal and the termination of flips

Abstract

In this paper, we develop a theory of diminished multiplier ideals on singular varieties which was introduced by Hacon, and developed by Lehmann. We prove a result regarding the termination of certain type of flips with scaling of an ample divisor if the Cartier index is bounded, and if ${\kappa }_{\sigma }(K_X+\Delta )\ge \dim X-1$ holds. The proof uses a theory of diminished multiplier ideal.

Comments are welcome. There is a major revision on this paper, especially Section 3