Pullbacks of hyperplane sections for Lagrangian fibrations are primitive

Abstract

Let p: M -> B be a Lagrangian fibration on a hyperkahler manifold of maximal holonomy (also known as IHS), and H the generator of the Picard group of B. We prove that the pullback $p^{\ast }(H)$ is a primitive class on M.

arXiv comment9 pages, v. 4.0, published version with minor corrections; proof of Theorem 3.1 simplified, claim 4.5 corrected

References in corpus (1)

• Base manifolds for fibrations of projective irreducible symplectic manifolds

Cited by in corpus (1)

• Computing Riemann-Roch polynomials and classifying hyper-Kähler fourfolds