Pullbacks of hyperplane sections for Lagrangian fibrations are primitive

preprint2020arXivOpen access

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∗(H)p^*(H) is a primitive class on M.

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