Abstract:
The Nash Blow up of an algebraic variety is defined as the Zariski closure of the graph of the map that sends every smooth point of the variety to its tangent space, seen as a point in a Grassmannian. The concept provides an alternative approach to the notorious and difficult problem of the resolution of singularities.
The talk will be a summary of known results concerning the Nash blow up: When does it resolve the variety, how to write it as a "classical" blow up of the variety along a suitable center, examples where it does not resolve the singularities.