English

Non-vanishing theorem for log canonical pairs

Algebraic Geometry 2009-12-01 v3

Abstract

We obtain a correct generalization of Shokurov's non-vanishing theorem for log canonical pairs. It implies the base point free theorem for log canonical pairs. We also prove the rationality theorem for log canonical pairs. As a corollary, we obtain the cone theorem for log canonical pairs. We do not need Ambro's theory of quasi-log varieties.

Keywords

Cite

@article{arxiv.0901.0409,
  title  = {Non-vanishing theorem for log canonical pairs},
  author = {Osamu Fujino},
  journal= {arXiv preprint arXiv:0901.0409},
  year   = {2009}
}

Comments

13 pages, v2: minor revisions, v3: minor revisions following referee's comments

R2 v1 2026-06-21T11:57:28.121Z