Related papers: Generalized quiver varieties and triangulated cate…

Toric quiver varieties (moduli spaces of quiver representations) are studied. Given a quiver and a weight there is an associated quasiprojective toric variety together with a canonical embedding into projective space. It is shown that for a…

We study the singularities of normalized R-matrices between arbitrary simple modules over the quantum loop algebra of type ADE in Hernandez--Leclerc's level-one subcategory using equivariant perverse sheaves, following the previous works by…

Let $X$ be a variety with an action by an algebraic group $G$. In this paper we discuss various properties of $G$-equivariant $D$-modules on $X$, such as the decompositions of their global sections as representations of $G$ (when $G$ is…

Any moduli space of representations of a quiver (possibly with oriented cycles) has an embedding as a dense open subvariety into a moduli space of representations of a bipartite quiver having the same type of singularities. A connected…

In type A we find equivalences of geometries arising in three settings: Nakajima's (``framed'') quiver varieties, conjugacy classes of matrices and loop Grassmannians. These are now all given by explicit formulas. In particular, we embedd…

We study tilting complexes over preprojective algebras of Dynkin type. We classify all tilting complexes by giving a bijection between tilting complexes and the braid group of the corresponding folded graph. In particular, we determine the…

To a finite quiver equipped with a positive integer on each of its vertices, we associate a holomorphic symplectic manifold having some parameters. This coincides with Nakajima's quiver variety with no stability parameter/framing if the…

We show that the representation type of the Jacobian algebra P(Q,S) associated to a 2-acyclic quiver Q with non-degenerate potential S is invariant under QP-mutations. We prove that, apart from very few exceptions, P(Q,S) is of tame…

We consider a generalization of representations of quivers that can be derived from the ordinary representations of quivers by considering a product of arbitrary classical groups instead of a product of the general linear groups and by…

In this paper, we give a complete classification of silted algebras for the quiver $\overrightarrow{\mathbb{A}}_{n}$ of type $\mathbb{A}_{n}$ with linear orientation and for the quiver obtained from $\overrightarrow{\mathbb{A}}_{n}$ by…

We generalize Derksen-Weyman-Zelevinsky's theory of quivers with potentials (QPs) to an $H$-based setting by considering quivers with exactly one loop at each vertex, asking the loops to be nilpotent and so attaching a truncated polynomial…

We compute the subgroup of the monodromy group of a generalized Kummer variety associated to equivalences of derived categories of abelian surfaces. The result was previously announced in arXiv:1201.0031. Mongardi showed that the subgroup…

We study silting objects over derived preprojective algebras of acyclic quivers by giving a direct relationship between silting objects, spherical twist functors and mutations. Especially, for a Dynkin quiver, we establish a bijection…

We study the bialgebra structures on quiver coalgebras and the monoidal structures on the categories of locally nilpotent and locally finite quiver representations. It is shown that the path coalgebra of an arbitrary quiver admits natural…

We first study the (canonical) orbit category of the bounded derived category of finite dimensional representations of a quiver with no infinite path, and we pay more attention on the case where the quiver is of infinite Dynkin type. In…

We study silting mutations (Okuyama-Rickard complexes) for selfinjective algebras given by quivers with potential (QPs). We show that silting mutation is compatible with QP mutation. As an application, we get a family of derived…

We use a geometric description of $m$-cluster categories of Dynkin type $A$ to count the the number of coloured quivers in the $m$-mutation class of quivers of Dynkin type $A$. This is related to angulations of polygons and the cell-growth…

Tannaka duality and its extensions by Lurie, Sch\"appi et al. reveal that many schemes as well as algebraic stacks may be identified with their tensor categories of quasi-coherent sheaves. In this thesis we study constructions of cocomplete…

We study quantum geometry of Nakajima quiver varieties of two different types - framed A-type quivers and ADHM quivers. While these spaces look completely different we find a surprising connection between equivariant K-theories thereof with…

In this paper we consider a construction in an arbitrary triangulated category T which resembles the notion of a Moore spectrum in algebraic topology. Namely, given a compact object C of T satisfying some finite tilting assumptions, we…