Degenerations of Grassmannians via Lattice Configurations

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 l...

Full description

Saved in:
Bibliographic Details
Published in:International mathematics research notices 2023-01, Vol.2023 (1), p.298-349
Main Authors: He, Xiang, Zhang, Naizhen
Format: Article
Language:English
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:1073-7928
1687-0247
DOI:10.1093/imrn/rnab241