Base manifolds for fibrations of projective irreducible symplectic manifolds

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 $X$.

References in corpus (1)

• Characteristic foliation on the discriminantal hypersurface of a holomorphic Lagrangian fibration

Cited by in corpus (2)

• Picard number of the generic fiber of an abelian fibered hyperkaehler manifold
• Positivity of Thom polynomials II: the Lagrange singularities