Collecting a few results from previous posts which, when taken together, seem to imply the results in the “germs” post hold more general when globalized (so for instance you could run the log-MMP in a family of surfaces over \mathbb{Z} .)

MMAT0.1b_copy 11/25/2015

MMAT0.1     12/3/2015 (probably reasonably complete version)

 

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