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arXiv · 2108.00993

Special MMP for log canonical generalised pairs

Vladimir Lazić·Nikolaos Tsakanikas·with an appendix joint with Xiaowei Jiang
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Abstract

We show that minimal models of $\mathbb{Q}$-factorial NQC log canonical generalised pairs exist, assuming the existence of minimal models of smooth varieties. More generally, we prove that on a $\mathbb{Q}$-factorial NQC log canonical generalised pair $ (X,B+M) $ we can run an MMP with scaling of an ample divisor which terminates, assuming that it admits an NQC weak Zariski decomposition or that $K_X+B+M$ is not pseudoeffective. As a consequence, we establish several existence results for minimal models and Mori fibre spaces.

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Vladimir Lazić, Nikolaos Tsakanikas, with an appendix joint with Xiaowei Jiang. 2021-08-02. Special MMP for log canonical generalised pairs. https://doi.org/10.1007/s00029-022-00798-8

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