P-trivial MMP, Zariski decompositions and minimal models for generalised pairs

2025/01/13 by Hu, Zhengyu
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2501.07551

Abstract

We develop a theory of P-trivial MMP whose each step is P-trivial for a given nef divisor P. As an application, we prove that, given a projective generalised klt pair (X,B+M) with data M' being just a nef ℝ-divisor, if K_X+B+M birationally has a Nakayama-Zariski decomposition with nef positive part, and either if M' or the positive part is log numerically effective, then it has a minimal model. Furthermore, we prove this for generalised lc pairs in dimension 3. This is a generalisation of the main theorem of [Birkar-Hu14]. We also prove some related results.

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