### Article

## Homological approach to the Hernandez-Leclerc construction and quiver varieties

In a previous paper the authors have attached to each Dynkin quiver an associative algebra.

The definition is categorical and the algebra is used to construct

desingularizations of arbitrary quiver Grassmannians. In the present paper we prove that this algebra is isomorphic to an algebra constructed by Hernandez-Leclerc defined combinatorially and used to describe certain

graded Nakajima quiver varieties. This approach is used to get an explicit realization of the

orbit closures of representations of Dynkin quivers as affine quotients.

The definition is categorical and the algebra is used to construct

desingularizations of arbitrary quiver Grassmannians. In the present paper we prove that this algebra is isomorphic to an algebra constructed by Hernandez-Leclerc defined combinatorially and used to describe certain

graded Nakajima quiver varieties. This approach is used to get an explicit realization of the

orbit closures of representations of Dynkin quivers as affine quotients.In a previous paper the authors have attached to each Dynkin quiver an associative algebra. The definition is categorical and the algebra is used to construct desingularizations of arbitrary quiver Grassmannians. In the present paper we prove that this algebra is isomorphic to an algebra constructed by Hernandez-Leclerc defined combinatorially and used to describe certain graded Nakajima quiver varieties. This approach is used to get an explicit realization of the orbit closures of representations of Dynkin quivers as affine quotients. - See more at: http://www.ams.org/journals/ert/2014-18-01/S1088-4165-2014-00449-7/home.html#sthash.TNXUywGF.dpuf