相关论文: Quiver representations arising from degenerations …

We describe all the schematic limits of families of divisors associated to a given family of rank-$r$ linear series on a one-dimensional family of projective varieties degenerating to a connected reduced projective scheme $X$ defined over…

Degenerations of linear series on smooth projective varieties approaching multicomponent varieties $X$ give rise to certain quiver representations in the category of linear series over $X$, which yield rational maps from $X$ to the…

We define linear degenerations of Schubert varieties via a special class of quiver Grassmannians. To do so, we restrict our study to an appropriate subvariety in the variety of representations of the considered quiver and describe a base…

Linear degenerate flag varieties are degenerations of flag varieties as quiver Grassmannians. For type A flag varieties, we obtain characterizations of flatness, irreducibility and normality of these degenerations via rank tuples. Some of…

Quiver Grassmannians are varieties parametrizing subrepresentations of a quiver representation. It is observed that certain quiver Grassmannians for type A quivers are isomorphic to the degenerate flag varieties investigated earlier by the…

We give an explicit combinatorial description of the deformation theory of the Abelian category of (quasi)coherent sheaves on any separated Noetherian scheme $X$ via the deformation theory of path algebras of quivers with relations, by…

This is a survey article for "Handbook of Linear Algebra", 2nd ed., Chapman & Hall/CRC, 2014. An informal introduction to representations of quivers and finite dimensional algebras from a linear algebraist's point of view is given. The…

We introduce the notion of (twisted) quiver representations in abelian categories and study the category of such representations. We construct standard resolutions and coresolutions of quiver representations and study basic homological…

Local models of Shimura varieties in type A can be realized inside products of Grassmannians via certain linear algebraic conditions. Laumon suggested a generalization which can be identified with a family over a line whose general fibers…

Linear free divisors are free divisors, in the sense of K.Saito, with linear presentation matrix (example: normal crossing divisors). Using techniques of deformation theory on representations of quivers, we exhibit families of linear free…

In this text, we characterize the representation type of an acyclic quiver by the properties of its associated quiver Grassmannians. This characterization utilizes and extends known results about singular quiver Grassmannians and cell…

We study minimal degenerations between preprojective modules over wild quivers. Asymptotic properties of such degenerations are studied, with respect to codimension and numbers of indecomposable direct summands. We provide families of…

We study minimal disjoint degenerations for representations of tame quivers. In particular, we prove that their codimensions are bounded by 2. Therefore a quiver is Dynkin resp. Euclidean resp. wild iff the codimensions are 1 resp. bounded…

Let $n \geq 2$. We introduce the notion of $n$-representations of quivers, and we explicitly provide concrete examples of $2$-representations of quivers. We establish the categories of $n$-representations and investigate kernels and…

In this paper, we introduce Schubert decompositions for quiver Grassmannians and investigate example classes of quiver Grassmannians with a Schubert decomposition into affine spaces. The main theorem puts the cells of a Schubert…

We describe the derived Picard groups and two-term silting complexes for quasi-hereditary algebras with two simple modules. We also describe by quivers with relations all algebras derived equivalent to a quasi-hereditary algebra with two…

A monoid structure on families of representations of a quiver is introduced by taking extensions of representations in families, i.e. subvarieties of the varieties of representations. The study of this monoid leads to interesting…

Several moduli spaces parametrizing linear subspaces of the projective space are cut out by linear and quadratic equations in their natural embedding: Grassmannians, Flag varieties, and Schubert varieties. The goal of this paper is to prove…

We discuss degenerations of symplectic and orthogonal representations of symmetric quivers and algebras with self-dualities. As in the non-symmetric case, we define a partial ordering, that we call symmetric Ext-order which gives a…

For semisimple Lie superalgebras over an algebraically closed field of characteristic zero, whose category of finite dimensional super representations is semisismple, we classify all irreducible super representations for which the…