Advanced Studies in Pure Mathematics

On log canonical rings

Osamu Fujino and Yoshinori Gongyo

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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.

Article information

Source
Higher Dimensional Algebraic Geometry: In honour of Professor Yujiro Kawamata's sixtieth birthday, K. Oguiso, C. Birkar, S. Ishii and S. Takayama, eds. (Tokyo: Mathematical Society of Japan, 2017), 159-169

Dates
Received: 8 March 2013
Revised: 12 July 2014
First available in Project Euclid: 23 October 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1540319486

Digital Object Identifier
doi:10.2969/aspm/07410159

Mathematical Reviews number (MathSciNet)
MR3791212

Zentralblatt MATH identifier
1388.14058

Subjects
Primary: 14E30: Minimal model program (Mori theory, extremal rays)

Citation

Fujino, Osamu; Gongyo, Yoshinori. On log canonical rings. Higher Dimensional Algebraic Geometry: In honour of Professor Yujiro Kawamata's sixtieth birthday, 159--169, Mathematical Society of Japan, Tokyo, Japan, 2017. doi:10.2969/aspm/07410159. https://projecteuclid.org/euclid.aspm/1540319486


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