Degenerations of Grassmannians via lattice configurations

Abstract

We study degenerations of Grassmannians constructed using convex lattice configurations in Bruhat-Tits buildings. Using techniques from quiver representations, we analyze their special fibers, which are explicitly described as quiver Grassmannians. For a class of lattice configurations, called the locally linearly independent configurations, we show that our construction coincide with Mustafin degenerations, thus generalizing a result of Faltings. In such cases, our analysis of special fibers also generalizes results of Cartwright et al. As an application, we prove a smoothing criterion for limit linear series on arbitrary reducible nodal curves.

Final version, to appear in IMRN

References in corpus (2)

• The Kodaira dimensions of ${\overline{\mathcal{M}}}_{22}$ and ${\overline{\mathcal{M}}}_{23}$
• Local models, Mustafin varieties and semi-stable resolutions

Cited by in corpus (2)

• Valued rank-metric codes
• One-parameter families of multiview varieties via quotient lattices