Giovanni Cerulli-Irelli

I will report on a joint project with Evgeny Feigin and Markus Reineke. Our starting point is the realization of degenerate flag varieties of type A, introduced and studied by Feigin-Littelmann-Fourier in order to produce a closed formula for the  q-character of an irreducible highest weight representation of sl_n (with respect to the PBW filtration), as particular quiver Grasmannians. Recall that given a quiver Q and a Q-representation M the quiver Grassmannian Gr_e(M) is the projective variety of all subrepresentation of M of dimension vector e.  In particular, Feigin and Finkelberg realize a desingularization of degenerate flag varieties of type A. We hence reinterpret that desingularization in terms of quivers, and we generalize it for all Dynkin quivers Q and all Q-representations. This construction has connection with the work of Keller-Scherotzke and  Leclerc-Plamondon, concering the study of Nakajima graded quiver varieties.