8 feb 2016 -- 16:30
Aula B, Dip. Matematica, Università "La Sapienza", Roma
Abstract.
Quiver Grassmannians are the natural generalization in the world of quivers of the usual Grassmannians of linear subspaces: given a representation M of a quiver Q and a dimension vector e, the quiver Grassmannians Gre(M) parametrizes subrepresentations of M of dimension vector e. We say that a quiver Grassmannian is of Dynkin type, if it is associated with a complex representation of a Dynkin quiver (i.e. an orientation of a simply--laced Dynkin diagram). In this lectures I will extensively recall the representation theory of (Dynkin) quivers. Then I will introduce quiver Grassmannians and some of their properties. Notice that every projective variety can be realized as a quiver Grassmannian, so we cannot expect to find general results. We will instead restrict our attention to "generic" quiver Grassmannians of Dynkin type and we will prove several interesting geometric properties. Those varieties include flag varieties and some Schubert varieties of type A.
Place: Aula B
When: Monday from 2:30pm--4:30pm
First lecture from 4:30pm