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Corpus ID: 199064306

Normal completions of toric varieties over rank one valuation rings and completions of $Γ$-admissible fans

@article{Friedenberg2019NormalCO,
title={Normal completions of toric varieties over rank one valuation rings and completions of \$Γ\$-admissible fans},
author={Netanel Friedenberg},
journal={arXiv: Algebraic Geometry},
year={2019}
}

We show that any normal toric variety over a rank one valuation ring admits an equivariant open embedding in a normal toric variety which is proper over the valuation ring, after a base-change by a finite extension of valuation rings. If the value group $\Gamma$ is discrete or divisible then no base-change is needed. We give explicit examples which show that existing methods do not produce such normal equivariant completions. Our approach is combinatorial and proceeds by showing that $\Gamma… Expand