تقرير
Semi-homogeneous vector bundles on abelian varieties: moduli spaces and their tropicalization
| العنوان: | Semi-homogeneous vector bundles on abelian varieties: moduli spaces and their tropicalization |
|---|---|
| المؤلفون: | Gross, Andreas, Kaur, Inder, Ulirsch, Martin, Werner, Annette |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Algebraic Geometry |
| الوصف: | We construct a moduli space of semi-homogeneous vector bundles with a fixed N\'eron-Severi class $H$ on an abelian variety $A$ over an algebraically closed field of characteristic zero. When $A$ has totally degenerate reduction over a non-Archimedean field, we describe our moduli space from the perspective of non-Archimedean uniformization and show that the essential skeleton may be identified with a tropical analogue of this moduli space. For $H=0$ our moduli space may be identified with the moduli space $M_{0,r}(A)$ of semistable vector bundles with vanishing Chern classes on $A$. In this case we construct a surjective analytic morphism from the character variety of the analytic fundamental group of $A$ onto $M_{0,r}(A)$, which naturally tropicalizes. One may view this construction as a non-Archimedean uniformization of $M_{0,r}(A)$. Comment: v2: added further explanation to Section 1, 31 pages, comments very welcome! |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2312.12980 |
| رقم الأكسشن: | edsarx.2312.12980 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |