For a finite subgroup $\Gamma\subset\mathrm {SL}(2,\mathbb {C}) $ and $ n\geq 1$, we
construct the (reduced scheme underlying the) Hilbert scheme of $ n $ points on the …

Inspired by recent work of Hernandez–Leclerc and Leclerc–Plamondon we investigate the
link between Nakajima's graded affine quiver varieties associated with an acyclic connected …

We study the geometry and topology of Hilbert schemes of points on the orbifold surface,
respectively the singular quotient surface, where is a finite subgroup of type A or D. We give …

For a finite subgroup $\Gamma\subset {\rm SL}(2,{\mathbb C}) $, we identify fine moduli
spaces of certain cornered quiver algebras, defined in earlier work, with orbifold Quot …

This article is an extended version of a minicourse given at the workshop of the 14th
International Conference on Representations of Algebras (ICRA XIV), held in August 2010 in …

We show that isomorphism classes of indecomposable-rigid pairs over, the preprojective
algebra of, are in bijection with internal-simplices in the prism, the product of an-simplex with …

We investigate several types of Nakajima quiver varieties and their connection to the
Kleinian singularities 𝐂 2/Γ. Such quiver varieties have many good properties: they are for …

This article is an extended version of the minicourse given by the second author at the
summer school of the conference Interactions of quantum affine algebras with cluster …

Let $\Gamma\in\mathrm {SL} _2 (\mathbb {C}) $ be a finite subgroup. We introduce a class
of projective noncommutative surfaces $\mathbb {P}^ 2_I $, indexed by a set of irreducible …

We realize geometrically a family of simple modules of (shifted) quantum loop groups
including Kirillov-Reshetikhin and prefundamental representations. To do this, we introduce …