Twisted cotangent bundles of Hyperkähler manifolds

Abstract

Let $X$ be a Hyperkähler manifold, and let $H$ be an ample divisor on $X$. We give a lower bound in terms of the Beauville-Bogomolov form $q(H)$ for the twisted cotangent bundle ${\Omega }_X\otimes H$ to be pseudoeffective. If $X$ is deformation equivalent to the Hilbert scheme of a K3 surface the lower bound can be written down explicitly and we study its optimality.

26 pages