%0 Journal Article %T Stability of tautological vector bundles on Hilbert squares of surfaces %A Ulrich Schlickewei %J Mathematics %D 2009 %I arXiv %X We prove stability of rank two tautological bundles on the Hilbert square of a surface (under a mild positivity condition) and compute their Chern classes. %U http://arxiv.org/abs/0909.1888v1