Technion
 
Mathematics Colloquium

PLEASE NOTE: This the first of TWO colloquia on 2/1/12.  
 
Speaker: Dmitry Kerner (University of Toronto)
 
Title: Local geometry of singular varieties
 
Time: Monday, January 2, 3:30 pm
 
Place: Amado 232
 
Colloquium homepage:  <http://www.technion.ac.il/~yehuday/colloquium/colloq.html>
 
Abstract:
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 number.
 
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.
 
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Technion Math. Net (TECHMATH)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from: Amir Yehudayoff   <amir.yehudayoff@gmail.com>