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

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References

SHOWING 1-10 OF 18 REFERENCES
Classification of normal toric varieties over a valuation ring of rank one
  • 15
  • PDF
Nagata's compactification theorem for normal toric varieties over a valuation ring of rank one
  • 2
  • PDF
Stable modification of relative curves
  • 45
  • PDF
A guide to tropicalizations
  • 74
  • PDF
Altered local uniformization of Berkovich spaces
  • 4
  • PDF
Completions of fans
  • 10
  • PDF
Lectures on Polytopes
  • 3,053
  • Highly Influential
  • PDF
Algebraic Number Theory
  • 2,298
  • PDF
Model theory : an introduction
  • 713
Toric Varieties , volume 124 of Graduate Studies in Mathematics
  • Combinatorial Convexity and Algebraic Geometry , volume 168 of Graduate Texts in Mathematics
  • 2011
...
1
2
...