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arXiv · 0711.3224

Base manifolds for fibrations of projective irreducible symplectic manifolds

Jun-Muk Hwang
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Abstract

Given a projective irreducible symplectic manifold $M$ of dimension $2n$, a projective manifold $X$ and a surjective holomorphic map $f:M \to X$ 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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Jun-Muk Hwang. 2007-11-20. Base manifolds for fibrations of projective irreducible symplectic manifolds. https://doi.org/10.1007/s00222-008-0143-9

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