Geometry of quiver Grassmannians of Dynkin type with applications to cluster algebras

  • Giovanni Cerulli Irelli

    Università di Roma La Sapienza, Italy
Geometry of quiver Grassmannians of Dynkin type with applications to cluster algebras cover
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Abstract

The paper includes a new proof of the fact that quiver Grassmannians associated with rigid representations of Dynkin quivers do not have cohomology in odd degrees. Moreover, it is shown that they do not have torsion in homology. A new proof of the Caldero–Chapoton formula is provided. As a consequence a new proof of the positivity of cluster monomials in the acyclic clusters associated with Dynkin quivers is obtained. The methods used here are based on joint works with Markus Reineke and Evgeny Feigin.