Degenerations of toric varieties over valuation rings
arXiv:1508.04057 · doi:10.1112/blms/bdw046
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.
13 pages. v3: Added Example 4.1.8 and new references. To appear in Bulletin of the London Mathematical Society