School of Mathematical Sciences
Monday, January 2, 2012
Schreiber 006, 12:15
University of Toronto
Local geometry of singular varieties
Singular varieties occur everywhere. Two natural ways to study them are to
deform (to smoothen) or to resolve the singularities. It is natural to compare
the invariants of the singular variety and of its smooth fellows.
This defines various invariants of singular varieties.
The fundamental topological invariant is the Milnor number (the defect of the
topological Euler characteristic). The fundamental geometric invariant is the
singularity genus (the defect of the holomorphic Euler characteristic). An old
conjecture, [Durfee 1978], bounds the singularity genus in terms of the Milnor
I will start from the general introduction to non-smooth varieties and then
proceed to the recent advances in the study of these invariants. Jointly with
A.Nemethi, we constructed series of counterexamples, violating the conjecture,
even asymptotically. Further, we succeeded to formulate a corrected
version, which is asymptotically sharp, and proved this version for a big
class of singularities.
Coffee will be served at 12:00 before the lecture
at Schreiber building 006