English

On quasi-log schemes

Algebraic Geometry 2022-08-17 v4

Abstract

The notion of quasi-log schemes was first introduced by Florin Ambro in his epoch-making paper: Quasi-log varieties. In this paper, we establish the basepoint-free theorem of Reid--Fukuda type for quasi-log schemes in full generality. Roughly speaking, it means that all the results for quasi-log schemes claimed in Ambro's paper hold true. The proof is Kawamata's X-method with the aid of the theory of basic slc-trivial fibrations. For the reader's convenience, we make many comments on the theory of quasi-log schemes in order to make it more accessible.

Cite

@article{arxiv.2107.04757,
  title  = {On quasi-log schemes},
  author = {Osamu Fujino},
  journal= {arXiv preprint arXiv:2107.04757},
  year   = {2022}
}

Comments

25 pages, v2: very minor revision, v3: revisions following referee's comments, v4: typos were corrected. arXiv admin note: text overlap with arXiv:2102.11986, arXiv:2105.14531

R2 v1 2026-06-24T04:03:46.856Z