Seminario de Geometría y Topología
Expositor: Dylan Rupel (Michigan State University)

Resumen: Varieties of quiver representations, known as quiver Grassmannians, are the main geometric object featuring in the categorification of cluster algebras. Reineke has shown that all projective varieties can be realized as quiver Grassmannians, so a uniform understanding of their geometry is highly unlikely.  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.