Mustafin degenerations

TL;DR

This paper generalizes Mustafin degenerations from projective space to arbitrary flag types, analyzing their structure, special fibers, and component behavior under natural projections in the context of Bruhat-Tits buildings.

Contribution

It extends the construction of Mustafin degenerations to all flag types and investigates their geometric properties and morphisms.

Findings

Analysis of reducedness of the special fiber

Behavior of components under projection morphisms

Generalization from projective space to arbitrary flag types

Abstract

A Mustafin degeneration is a degeneration of a flag variety induced by a vertex configuration in the Bruhat-Tits building of the projective linear group over a field with a non-archimedean discrete valuation. In the case where the flag type is projective space, Mustafin degenerations have been studied previously. We generalize the construction to the case of arbitrary flag types. We examine the special fiber of a Mustafin degeneration for reducedness and study the behavior of its components under a natural projection morphism between Mustafin degenerations, which arises from the inclusion of flags.