On log canonical rings. (English) Zbl 1388.14058

Fujino, Osamu; Gongyo, Yoshinori

Oguiso, Keiji (ed.) et al., Higher dimensional algebraic geometry. In honour of Professor Yujiro Kawamata’s sixtieth birthday. Proceedings of the conference, Tokyo, Japan, January 7–11, 2013. Tokyo: Mathematical Society of Japan (MSJ) (ISBN 978-4-86497-046-4/hbk). Advanced Studies in Pure Mathematics 74, 159-169 (2017).

Summary: We discuss the relationship among various conjectures in the minimal model theory including the finite generation conjecture of the log canonical rings and the abundance conjecture.
In particular, we show that the finite generation conjecture of the log canonical rings for log canonical pairs can be reduced to that of the log canonical rings for purely log terminal pairs of log general type.
For the entire collection see [Zbl 1388.14012].

MSC:

14E30	Minimal model program (Mori theory, extremal rays)
14C20	Divisors, linear systems, invertible sheaves