Special Kähler geometry and holomorphic Lagrangian fibrations
arXiv:2308.10553 · doi:10.5802/crmath.629
Abstract
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.
arXiv comment32 pages; final version to appear in the Demailly memorial volume of Comptes Rendus Mathematique
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