Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 298-349 |
| Seitenumfang | 52 |
| Fachzeitschrift | International Mathematics Research Notices |
| Jahrgang | 2023 |
| Ausgabenummer | 1 |
| Frühes Online-Datum | 1 Okt. 2021 |
| Publikationsstatus | Veröffentlicht - Jan. 2023 |
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.
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in: International Mathematics Research Notices, Jahrgang 2023, Nr. 1, 01.2023, S. 298-349.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Degenerations of Grassmannians via Lattice Configurations
AU - He, Xiang
AU - Zhang, Naizhen
N1 - Funding Information: This work was supported by the European Research Council Consolidator Grant 770922— BirNonArchGeom [to X.H.]; the Deutsche Forschungsgemeinschaft Priority Programme 2026 “Geometry at infinity” [to N.Z.]; and the Methusalem Project Pure Mathematics at KU Leuven during the preparation of an earlier version of this work [to N.Z.].
PY - 2023/1
Y1 - 2023/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85152209313&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1910.08163
DO - 10.48550/arXiv.1910.08163
M3 - Article
AN - SCOPUS:85152209313
VL - 2023
SP - 298
EP - 349
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
SN - 1073-7928
IS - 1
ER -