Rigid hyperholomorphic sheaves remain rigid along twistor deformations of the underlying hyparkahler manifold

Eyal Markman, Sukhendu Mehrotra, Misha Verbitsky

Let S be a K3 surface and M a smooth and projective 2n-dimensional moduli space of stable coherent sheaves on S. Over M x M there exists a rank 2n-2 reflexive hyperholomorphic shea…