On diminished multiplier ideal and the termination of flips

2024/05/20 by Donghyeon Kim, Kim, Donghyeon
Mathematics · #14E30 #14F18 #Algebraic Geometry (math.AG) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2405.11902

openalex publication_date 2024/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 κ_σ(K_X+Δ)≥ dim X-1 holds. The proof uses a theory of diminished multiplier ideal.

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