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A configuration space of representationsGeometry/Topology
|Speaker: ||Eric Babson, UC Davis|
|Location: ||2112 MSB|
|Start time: ||Wed, Nov 29 2006, 4:10PM|
To every directed graph and ring is associated a path algebra with an
ideal generated by the edges.
I will define a space parametrizing the quotient modules of a certain projective
(associated to weights on the vertices) which are finite dimensional and annihilated
by some power of the edge ideal. Every such representation arises as one of these
quotients for sufficiently large projectives.
Topologically, these spaces have pavings by rational varieties, specifically
affine bundles over iterated Grassmannian bundles which are well understood.
Less clear is the topology of the closures of these parts.
I will say something about attempts to use momentum maps to get at the
topology of these closures.
The spaces can also be seen as intersections of Springer varieties.