The Michigan Mathematical Journal

Nagata’s Compactification Theorem for Normal Toric Varieties over a Valuation Ring of Rank One

Alejandro Soto

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Using invariant Zariski–Riemann spaces, we prove 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.

Article information

Michigan Math. J., Volume 67, Issue 1 (2018), 99-116.

Received: 9 August 2016
Revised: 5 April 2017
First available in Project Euclid: 26 October 2017

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Zentralblatt MATH identifier

Primary: 14M25: Toric varieties, Newton polyhedra [See also 52B20] 14L30: Group actions on varieties or schemes (quotients) [See also 13A50, 14L24, 14M17] 13F30: Valuation rings [See also 13A18]


Soto, Alejandro. Nagata’s Compactification Theorem for Normal Toric Varieties over a Valuation Ring of Rank One. Michigan Math. J. 67 (2018), no. 1, 99--116. doi:10.1307/mmj/1508983384.

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