Anticanonical minimal models and Zariski decomposition

Sungwook Jang

Anticanonical minimal models and Zariski decomposition

Algebraic Geometry 2025-06-06 v2

Authors: Sungwook Jang

Abstract

Birkar and Hu showed that if a pair $(X,\Delta)$ is lc and $K_{X}+\Delta$ admits a birational Zariski decomposition, then $(X,\Delta)$ has a minimal model. Analogously, we prove that if a pair $(X,\Delta)$ is pklt and $-(K_{X}+\Delta)$ admits a birational Zariski decomposition, then $(X,\Delta)$ has an anticanonical minimal

Cite

@article{arxiv.2405.10533,
  title  = {Anticanonical minimal models and Zariski decomposition},
  author = {Sungwook Jang},
  journal= {arXiv preprint arXiv:2405.10533},
  year   = {2025}
}

Comments

In previous version, there was a mistake when we apply the theorem of Birkar and Hu. So I revised section 4 and added Lemma 4.3

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