Abstract:

Moduli spaces of stable sheaves (and stable complexes) on K3 surfaces are a well-studied family of high-dimensional algebraic varieties. An important classical theorem says that they are projective hyperkähler varieties that are deformation equivalent to the punctual Hilbert scheme on a K3 surface. In this talk I will introduce these objects, and describe a new proof of this result that uses wall-crossing with respect to Bridgeland stability conditions.