Base manifolds for fibrations of projective irreducible symplectic manifolds

Details Base manifolds for fibrations of projective irreducible symplectic manifolds Base manifolds for fibrations of projective irreducible symplectic manifolds

2007-11-20

arxiv.org/abs/0711.3224v1

Mathematics

Algebraic Geometry

Scientific paper

10.1007/s00222-008-0143-9

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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