Department of Mathematics

Seminar in Cluster algebras

  •  Dylan Rupel, MSU
  •  Cell Decompositions for Rank Two Quiver Grassmannians
  •  10/04/2018
  •  3:00 PM - 4:00 PM
  •  C117 Wells Hall

A quiver Grassmannian is a variety parametrizing subrepresentations of a given quiver representation. Reineke has shown that all projective varieties can be realized as quiver Grassmannians. In this talk, I will study a class of smooth projective varieties arising as quiver Grassmannians for (truncated) preprojective representations of an n-Kronecker quiver, i.e. a quiver with two vertices and n parallel arrows between them. The main result I will present is a recursive construction of cell decompositions for these quiver Grassmannians. If there is time I will discuss a combinatorial labeling of the cells by which their dimensions may conjecturally be directly computed. This is a report on joint work with Thorsten Weist.



Department of Mathematics
Michigan State University
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East Lansing, MI 48824

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