On minimal model program and Zariski decomposition of potential triples

2025/02/02 by Choi, Sung Rak, Jang, Sungwook, Lee, Dae-Won · 2 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2502.00790

Abstract

In this paper, we investigate properties of potential triples (X,Δ,D) which consists of a pair (X,Δ) and a pseudoeffective ℝ-Cartier divisor D. In particular, we show that if D admits a birational Zariski decomposition, then one can associate a generalized pair structure to the potential triple (X,Δ,D). Moreover, we can run the generalized MMP on (K_X+Δ+D) as special cases. As an application, we also show that for a pklt pair (X,Δ), if -(K_X+Δ) admits a birational Zariski decomposition with NQC positive part, then there exists a -(K_X+Δ)-minimal model.

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• K-stability of del Pezzo surfaces with a single quotient singularity
• A valuative approach to the anticanonical minimal model program

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