Algebraic Geometry Seminar
Chris Brav
U. of Toronto
Braid groups and Kleinian singularities
Abstract: We review the relation between the geometry of Kleinian singularities and Dynkin diagrams
of types ADE, recalling in particular the construction of a braid group
action of type A,D, or E on the derived category of coherent sheaves on the
minimal resolution of a Kleinian singularity. By work of Seidel-Thomas,
this action was known to be faithful in type A. We extend this faithfulness
result to types ADE and then promote this to a faithful action of an extended affine braid group of
the appropriate type. Our faithfulness results provide the missing
ingredient for completing Bridgeland's description of spaces of stability
conditions for certain triangulated categories associated to Kleinian
singularities.
This is joint work with Hugh Thomas from the University of New Brunswick.
Thursday January 28, 2010 at 4:00 PM in SEO 636