Abstract
We treat two different topics on the log minimal model program, especially for four-dimensional log canonical pairs:
(a) finite generation of the log canonical ring in dimension four,
(b) abundance theorem for irregular fourfolds.
We obtain (a) as a direct consequence of the existence of four-dimensional log minimal models by using Fukuda’s theorem on the four-dimensional log abundance conjecture. We can prove (b) only by using traditional arguments. More precisely, we prove the abundance conjecture for irregular -folds on the assumption that the minimal model conjecture and the abundance conjecture hold in dimension .
Citation
Osamu Fujino. "Finite generation of the log canonical ring in dimension four." Kyoto J. Math. 50 (4) 671 - 684, Winter 2010. https://doi.org/10.1215/0023608X-2010-010
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