English

On relative birational geometry and Nagata's compactification

Algebraic Geometry 2016-05-30 v2

Abstract

In 2011, the first author introduced (relative) Riemann-Zariski spaces corresponding to a morphism of schemes and established their basic properties. In this paper we clarify that theory and extend it to morphisms between algebraic spaces. As an application, a new proof of Nagata's compactification theorem for algebraic spaces is obtained.

Keywords

Cite

@article{arxiv.1311.6308,
  title  = {On relative birational geometry and Nagata's compactification},
  author = {Michael Temkin and Ilya Tyomkin},
  journal= {arXiv preprint arXiv:1311.6308},
  year   = {2016}
}

Comments

28 pages, comments are welcome

R2 v1 2026-06-22T02:14:17.797Z