Base manifolds for fibrations of projective irreducible symplectic manifolds

Hwang, Jun-Muk
December 2008
Inventiones Mathematicae;Dec2008, Vol. 174 Issue 3, p625
Academic Journal
Given a projective irreducible symplectic manifold M of dimension 2 n, 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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