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Foundations of the minimal model program. (English) Zbl 1386.14072
MSJ Memoirs 35. Tokyo: Mathematical Society of Japan (ISBN 978-4-86497-045-7/pbk). xv, 289 p. (2017).
In this book the author surveys the minimal model program for quasi-log schemes. Quasi-log schemes arise naturally in the context of the minimal model program, they generalize the non-klt locus of a log canonical pair. The main results discussed in this paper are the adjunction and vanishing theorems, the base point free theorem, the rationality theorem and the cone theorem for quasi-log schemes.

14E30 Minimal model program (Mori theory, extremal rays)
14F17 Vanishing theorems in algebraic geometry
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