English

On non-projective complete toric varieties

Algebraic Geometry 2025-07-15 v2

Abstract

For every complete toric variety, there exists a projective toric variety which is isomorphic to it in codimension one. In this paper, we show that every smooth non-projective complete toric threefold of Picard number at most five becomes projective after a finite succession of flops or anti-flips.

Keywords

Cite

@article{arxiv.2412.02392,
  title  = {On non-projective complete toric varieties},
  author = {Osamu Fujino and Hiroshi Sato},
  journal= {arXiv preprint arXiv:2412.02392},
  year   = {2025}
}

Comments

24 pages, v2: revisions following referee's comments and suggestions, to appear in Exp. Math

R2 v1 2026-06-28T20:21:16.282Z