On the non-vanishing conjecture and existence of log minimal models

Abstract

We prove that the non-vanishing conjecture and the log minimal model conjecture for projective log canonical pairs can be reduced to the non-vanishing conjecture for smooth projective varieties such that the boundary divisor is zero.

arXiv comment17 pages. final version. Remark 3.3 was added. To appear in Publ. Res. Inst. Math. Sci. arXiv admin note: text overlap with arXiv:1607.05005