Georgia Institute of Technology College of Sciences

After reviewing classical results about existence of completions of varieties, I will talk about a class of degenerations of toric varieties which have a combinatorial classification - normal toric varieties over rank one valuation rings. I will then discuss recent results about the existence of equivariant completions of such degenerations. In particular, I will show a result from my thesis about the existence of normal equivariant completions of these degenerations.

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