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arXiv · 1508.04057

Degenerations of toric varieties over valuation rings

Tyler Foster·Dhruv Ranganathan
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Abstract

We develop a theory of multi-stage degenerations of toric varieties over finite rank valuation rings, extending the Mumford--Gubler theory in rank one. Such degenerations are constructed from fan-like structures over totally ordered abelian groups of finite rank. Our main theorem describes the geometry of successive special fibers in the degeneration in terms of the polyhedral geometry of a system of recession complexes associated to the fan.

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Tyler Foster, Dhruv Ranganathan. 2015-08-17. Degenerations of toric varieties over valuation rings. https://doi.org/10.1112/blms/bdw046

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