# University of Toronto's Symplectic Geometry Seminar

March 29, 2004, 2:10 - 3 PM

SS5017A

## Andre Henriques

###
MIT

##
Orbifolds as stacks versus orbifolds as non-commutative spaces, and the
resolution of ADE surface singularities

** Abstract: **
The ADE surface singularities are the quotients of C^2 by finite
subgroups of SU2. They are very natural examples of complex orbifolds.
Their minimal resolutions Y->X carry the information of the corresponding
Dynkin diagram.
To make sense of the map Y->X, we usually view X and Y as varieties. But
in that context, X is clearly singular, which is contrary to the spirit of
orbifolds. Somehow, we should endow X with some structure that makes it
behave as if it were a smooth variety.
If we decide to view X as a smooth stack, then we notice that the map
Y->X doesn't exist any more, which is annoying. However, if we view X as a
non-commutative space, then the map X->Y does exist.