Mathematics Colloquia and Seminars

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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.