Dubrovin duality for open Hurwitz flat F-manifolds
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866917135394013184 |
|---|---|
| author | Proserpio, Alessandro Strachan, Ian A. B. |
| author_facet | Proserpio, Alessandro Strachan, Ian A. B. |
| contents | We prove that the Dubrovin dual of a Hurwitz Frobenius manifold extends naturally to an F-manifold with compatible flat connection on the universal curve, in the sense of the open WDVV equations. A similar result is proven for the Frobenius manifold itself in arXiv:2503.09258 . This equips the universal curve with two F-manifolds with compatible flat structure, and we study their duality. We show that they combine into a bi-flat F-manifold. Conditions on open WDVV solutions imposed in previous work are retrieved in this setting, thus providing them with a geometrical meaning. Finally, explicit examples are computed. For Saito Frobenius manifolds of types $A$ and $D$, the extended prepotentials coincide with open WDVV solutions computed independently, whereas even the existence of the solution in type $E$ had not been previously discussed. On the other hand, new non-homogeneous solutions are constructed by duality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_08795 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dubrovin duality for open Hurwitz flat F-manifolds Proserpio, Alessandro Strachan, Ian A. B. Mathematical Physics Differential Geometry Exactly Solvable and Integrable Systems 53D45 (Primary) 37K10, 14H70 (Secondary) We prove that the Dubrovin dual of a Hurwitz Frobenius manifold extends naturally to an F-manifold with compatible flat connection on the universal curve, in the sense of the open WDVV equations. A similar result is proven for the Frobenius manifold itself in arXiv:2503.09258 . This equips the universal curve with two F-manifolds with compatible flat structure, and we study their duality. We show that they combine into a bi-flat F-manifold. Conditions on open WDVV solutions imposed in previous work are retrieved in this setting, thus providing them with a geometrical meaning. Finally, explicit examples are computed. For Saito Frobenius manifolds of types $A$ and $D$, the extended prepotentials coincide with open WDVV solutions computed independently, whereas even the existence of the solution in type $E$ had not been previously discussed. On the other hand, new non-homogeneous solutions are constructed by duality. |
| title | Dubrovin duality for open Hurwitz flat F-manifolds |
| topic | Mathematical Physics Differential Geometry Exactly Solvable and Integrable Systems 53D45 (Primary) 37K10, 14H70 (Secondary) |
| url | https://arxiv.org/abs/2512.08795 |