Special Kähler geometry and holomorphic Lagrangian fibrations
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914833191927808 |
|---|---|
| author | Li, Yang Tosatti, Valentino |
| author_facet | Li, Yang Tosatti, Valentino |
| contents | Given a holomorphic Lagrangian fibration of a compact hyperkahler manifold, we use the differential geometry of the special Kahler metric that exists on the base away from the discriminant locus, and show that the pullback of the tangent bundle of the base to the total space of a family of minimal rational curves admits a parallel splitting. The splitting is nontrivial when the base is not half-dimensional projective space. Combining this with results of Voisin, Hwang and Bakker-Schnell, we deduce that the base must be projective space, a result first proved by Hwang. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_10553 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Special Kähler geometry and holomorphic Lagrangian fibrations Li, Yang Tosatti, Valentino Algebraic Geometry Differential Geometry 14J42, 14D06, 14D07, 32G20, 53C25 Given a holomorphic Lagrangian fibration of a compact hyperkahler manifold, we use the differential geometry of the special Kahler metric that exists on the base away from the discriminant locus, and show that the pullback of the tangent bundle of the base to the total space of a family of minimal rational curves admits a parallel splitting. The splitting is nontrivial when the base is not half-dimensional projective space. Combining this with results of Voisin, Hwang and Bakker-Schnell, we deduce that the base must be projective space, a result first proved by Hwang. |
| title | Special Kähler geometry and holomorphic Lagrangian fibrations |
| topic | Algebraic Geometry Differential Geometry 14J42, 14D06, 14D07, 32G20, 53C25 |
| url | https://arxiv.org/abs/2308.10553 |