Geometric quantization of generalized Hirzebruch fibrations
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866912315870281728 |
|---|---|
| author | Piccirilli, Andrea |
| author_facet | Piccirilli, Andrea |
| contents | Hirzebruch surfaces, defined as the projectivization of line bundles over $\C\mathbb{P}^1$, support a toric action and thus represent an infinite class of symplectic toric manifolds of complex dimension 2. In this paper, an infinite class of toric manifolds given as projective bundles over $\mathbb{C}\mathbb{P}^d$ will be constructed for every complex dimension $d$ and it will be shown that each manifold supports a symplectic structure. With the toric and symplectic structure of the manifolds at our disposal, we then study their geometric quantization and how it relates to different values of the twisting parameter of the fibrations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_04975 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometric quantization of generalized Hirzebruch fibrations Piccirilli, Andrea Symplectic Geometry Mathematical Physics Hirzebruch surfaces, defined as the projectivization of line bundles over $\C\mathbb{P}^1$, support a toric action and thus represent an infinite class of symplectic toric manifolds of complex dimension 2. In this paper, an infinite class of toric manifolds given as projective bundles over $\mathbb{C}\mathbb{P}^d$ will be constructed for every complex dimension $d$ and it will be shown that each manifold supports a symplectic structure. With the toric and symplectic structure of the manifolds at our disposal, we then study their geometric quantization and how it relates to different values of the twisting parameter of the fibrations. |
| title | Geometric quantization of generalized Hirzebruch fibrations |
| topic | Symplectic Geometry Mathematical Physics |
| url | https://arxiv.org/abs/2504.04975 |