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...

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Bibliographic Details
Published in:arXiv.org 2021-09
Main Authors: He, Xiang, Zhang, Naizhen
Format: Article
Language:English
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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:2331-8422
DOI:10.48550/arxiv.1910.08163