Let be a polarized smooth projective surface satisfying , and let be either a rank 1 torsion-free sheaf or a rank 2 -stable vector bundle on . Assume that . This article shows that the rank 2—respectively, rank 4—tautological sheaf associated with on the Hilbert square is -stable with respect to a certain polarization.
"Stability of tautological bundles on the Hilbert scheme of two points on a surface." Nagoya Math. J. 214 79 - 94, June 2014. https://doi.org/10.1215/00277630-2416410