Stability and certain $$\mathbb {P}^n$$-functors

Abstract

AbstractLet X be a K3 surface. We prove that Addington’s $$\mathbb {P}^n$$ P n -functor between the derived categories of X and the Hilbert scheme of points $$X^{[k]}$$ X [ k ] maps stable vector bundles on X to stable vector bundles on $$X^{[k]}$$ X [ k ] , given some numerical conditions are satisfied.