Special Kähler geometry and holomorphic Lagrangian fibrations
Given a holomorphic Lagrangian fibration of a compact hyperkähler manifold, we use the differential geometry of the special Kähler 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 r...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Académie des sciences
2024-06-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.629/ |
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| Summary: | Given a holomorphic Lagrangian fibration of a compact hyperkähler manifold, we use the differential geometry of the special Kähler 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. |
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| ISSN: | 1778-3569 |