Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2201.08113 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- Let $R$ be a complete discrete valuation ring, $k(η)$ its fraction field, $S:={\rm Spec} R$, $(G_η,\mathcal{L}_η)$ a polarized abelian variety over $k(η)$ with $\mathcal{L}_η$ ample cubical and $\mathcal{G}$ the Néron model of $G_η$ over $S$. Suppose that $\mathcal{G}$ is totally degenerate semiabelian over $S$. Then there exists a (unique) relative compactification $(P,\mathcal{N})$ of $\mathcal{G}$ such that ($α$) $P$ is Cohen-Macaulay with codim$_P(P\setminus\mathcal{G}) = 2$ and ($β$) $\mathcal{N}$ is ample invertible with $\mathcal{N}_{|\mathcal{G}}$ cubical and $\mathcal{N}_η=\mathcal{L}^{\otimes n}_η$ for some positive integer $n$.