On log canonical rings

Abstract

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.

11 pages, v2: revision following referee's report, Appendix is new, the referee's proof of Lemma 3.2 is added