Generalized Jacobians of graphs
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918247902740480 |
|---|---|
| author | Jordan, Bruce W. Ribet, Kenneth A. Scholl, Anthony J. |
| author_facet | Jordan, Bruce W. Ribet, Kenneth A. Scholl, Anthony J. |
| contents | We define a generalized Jacobian $\mathrm{J}_\mathfrak{m}(\mathit{Gr})$ and a generalized Picard group $\mathrm{P}_\mathfrak{m}(\mathit{Gr})$ of a graph $\mathit{Gr}$ with respect to a modulus $ \mathfrak{m}=\sum_{i=1}^s m_iw_i$ with $w_i$ vertices of $\mathit{Gr}$ and $m_i\geq 1$. These groups occur as the component groups of Néron models of generalized Jacobians. We prove a universal mapping property for $\mathrm{J}_\mathfrak{m}(\mathit{Gr})$ and show that an Abel-Jacobi map in this context induces an isomorphism from $\mathrm{P}_\frak{m}(\mathit{Gr})$ to $\mathrm{J}_\mathfrak{m}(\mathit{Gr})$. We also reinterpret $\mathrm{P}_\mathfrak{m}(\mathit{Gr})$ in terms of sheaves on the geometric realization $\left| \mathit{Gr}\right|$ of $\mathit{Gr}$, making a connection with tropical geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_12041 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized Jacobians of graphs Jordan, Bruce W. Ribet, Kenneth A. Scholl, Anthony J. Combinatorics Algebraic Geometry Number Theory Primary 31C20, Secondary 05C38 We define a generalized Jacobian $\mathrm{J}_\mathfrak{m}(\mathit{Gr})$ and a generalized Picard group $\mathrm{P}_\mathfrak{m}(\mathit{Gr})$ of a graph $\mathit{Gr}$ with respect to a modulus $ \mathfrak{m}=\sum_{i=1}^s m_iw_i$ with $w_i$ vertices of $\mathit{Gr}$ and $m_i\geq 1$. These groups occur as the component groups of Néron models of generalized Jacobians. We prove a universal mapping property for $\mathrm{J}_\mathfrak{m}(\mathit{Gr})$ and show that an Abel-Jacobi map in this context induces an isomorphism from $\mathrm{P}_\frak{m}(\mathit{Gr})$ to $\mathrm{J}_\mathfrak{m}(\mathit{Gr})$. We also reinterpret $\mathrm{P}_\mathfrak{m}(\mathit{Gr})$ in terms of sheaves on the geometric realization $\left| \mathit{Gr}\right|$ of $\mathit{Gr}$, making a connection with tropical geometry. |
| title | Generalized Jacobians of graphs |
| topic | Combinatorics Algebraic Geometry Number Theory Primary 31C20, Secondary 05C38 |
| url | https://arxiv.org/abs/2512.12041 |