Abstract
Given a projective irreducible symplectic manifold M of dimension 2n, a projective manifold X and a surjective holomorphic map f:M→X with connected fibers of positive dimension, we prove that X is biholomorphic to the projective space of dimension n. The proof is obtained by exploiting two geometric structures at general points of X: the affine structure arising from the action variables of the Lagrangian fibration f and the structure defined by the variety of minimal rational tangents on the Fano manifold X.
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Mathematics Subject Classification (2000)
14J40, 14J45
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Hwang, JM. Base manifolds for fibrations of projective irreducible symplectic manifolds. Invent. math. 174, 625–644 (2008). https://doi.org/10.1007/s00222-008-0143-9
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DOI: https://doi.org/10.1007/s00222-008-0143-9