Hyperkahler Manifolds and Sheaves

摘要

Moduli spaces of hyperkahler manifolds or of sheaves on them are often non-separated. We will discuss results where this phenomenon reflects interesting geometric aspects, e.g. deformation equivalence of birational hyperkahler manifolds or cohomological properties of derived autoequivalences. In these considerations the Ricci-flat structure often plays a crucial role via the associated twistor space providing global deformations of manifolds and bundles.