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3-fold log models. (English) Zbl 0873.14014
The author improves the results of the log minimal model program (LMMP) on cones, contractions, flips, termination and abundance, proving them under the following more general conditions: (i) boundaries are $$\mathbb{R}$$-divisors (instead of $$\mathbb{Q}$$-divisors), (ii) singularities are log canonical (instead of log terminal).
The proofs are based both on the analogous theorems in the standard case and on vanishing theorems.

##### MSC:
 14E30 Minimal model program (Mori theory, extremal rays) 14J30 $$3$$-folds 14M07 Low codimension problems in algebraic geometry
##### Keywords:
log minimal model program; flips; abundance; vanishing theorems
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##### References:
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