English

On Tropical Compactifications

Algebraic Geometry 2009-02-13 v2

Abstract

We give an affirmative answer to a conjecture proposed by Tevelev in characteristic 0 case: any variety contains a sch\"on very affine open subvariety. Also we show that any fan supported on the tropicalization of a sch\"on very affine variety produces a sch\"on compactification. Using toric schemes over a discrete valuation ring, we extend tropical compatifications to the non-constant coefficient case.

Keywords

Cite

@article{arxiv.0902.2009,
  title  = {On Tropical Compactifications},
  author = {Mark Luxton and Zhenhua Qu},
  journal= {arXiv preprint arXiv:0902.2009},
  year   = {2009}
}

Comments

19 pages, comments are welcome

R2 v1 2026-06-21T12:10:28.613Z