The Hilbert scheme of n points on a manifold parametrizes length-n subschemes of M. On the one hand, this is a classifying space of finite codimension ideals in polynomial rings, on the other hand, being one of the most natural moduli spaces, it plays a major role in many classical problems in enumerative geometry, complex geometry and singularity theory.
While the geometry the Hilbert scheme of points on nonsingular surfaces has been the subject of intensive study during the last 50 years, our knowledge of this configuration space on higher dimensional manifolds and surfaces with
singularities is rather limited.
This workshop will focus on recent advances and emerging new methods in
this key area of modern geometry.
