Infinitesimal deformations of the tangent bundle of Hyperkahler manifolds

The tangent bundle of a hyperkahler manifold has very good deformation properties and therefore it is a natural candidate for constructing moduli spaces of (hyperholomorphic) sheaves. In this talk I will give an introduction to this topic and after I will focus on Hilbert schemes of points on a K3 surface. The main result is that in this case the tangent bundle turns out to be rigid. Joint work with Alessio Bottini. Please register with Christian Lehn. Corona restrictions at TU Chemnitz require a proof according to 3G-rule as well as wearing a FFP2 mask during the talk.