Nagata's compactification theorem for normal toric varieties over a valuation ring of rank one

Alejandro Soto

Nagata's compactification theorem for normal toric varieties over a valuation ring of rank one

Algebraic Geometry 2017-04-07 v2

Authors: Alejandro Soto

Abstract

We prove, using invariant Zariski-Riemann spaces, that every normal toric variety over a valuation ring of rank one can be embedded as an open dense subset into a proper toric variety equivariantly. This extends a well known theorem of Sumihiro for toric varieties over a field to this more general setting.

Keywords

Nagata compactification normal toric varieties valuation ring of rank one Zariski-Riemann spaces equivariant embedding Sumihiro's theorem

Cite

@article{arxiv.1608.02815,
  title  = {Nagata's compactification theorem for normal toric varieties over a valuation ring of rank one},
  author = {Alejandro Soto},
  journal= {arXiv preprint arXiv:1608.02815},
  year   = {2017}
}

Comments

1 figure, 14 pages. Few modifications after the comments of the referee. Accepted by the Michigan Mathematical Journal

Nagata's compactification theorem for normal toric varieties over a valuation ring of rank one

Abstract

Keywords

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