Foundations of the minimal model program. (English) Zbl 1386.14072

Fujino, Osamu

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.

Reviewer: Christopher Hacon (Salt Lake City)

MSC:

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

Keywords:

minimal model program; quasi-log schemes