Stability conditions for line bundles on nodal curves
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2023
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866909395204440064 |
|---|---|
| author | Pagani, Nicola Tommasi, Orsola |
| author_facet | Pagani, Nicola Tommasi, Orsola |
| contents | We introduce the abstract notion of a \emph{smoothable fine compactified Jacobian} of a nodal curve, and of a family of nodal curves whose general element is smooth. Then we introduce the notion of a combinatorial stability condition for line bundles and their degenerations. We prove that smoothable fine compactified Jacobians are in bijection with these stability conditions. We then turn our attention to \emph{fine compactified universal Jacobians}, that is, fine compactified Jacobians for the moduli space $\overline{\mathcal{M}}_g$ of stable curves (without marked points). We prove that every fine compactified universal Jacobian is isomorphic to the one first constructed by Caporaso, Pandharipande and Simpson in the nineties. In particular, without marked points, there exists no fine compactified universal Jacobian unless $\gcd(d+1-g, 2g-2)=1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_08509 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Stability conditions for line bundles on nodal curves Pagani, Nicola Tommasi, Orsola Algebraic Geometry Combinatorics 14H10, 14H40, 14K10, 14Txx We introduce the abstract notion of a \emph{smoothable fine compactified Jacobian} of a nodal curve, and of a family of nodal curves whose general element is smooth. Then we introduce the notion of a combinatorial stability condition for line bundles and their degenerations. We prove that smoothable fine compactified Jacobians are in bijection with these stability conditions. We then turn our attention to \emph{fine compactified universal Jacobians}, that is, fine compactified Jacobians for the moduli space $\overline{\mathcal{M}}_g$ of stable curves (without marked points). We prove that every fine compactified universal Jacobian is isomorphic to the one first constructed by Caporaso, Pandharipande and Simpson in the nineties. In particular, without marked points, there exists no fine compactified universal Jacobian unless $\gcd(d+1-g, 2g-2)=1$. |
| title | Stability conditions for line bundles on nodal curves |
| topic | Algebraic Geometry Combinatorics 14H10, 14H40, 14K10, 14Txx |
| url | https://arxiv.org/abs/2309.08509 |