Related papers: On Some Quiver Determinantal Varieties

We explain the bundle structures of the {\it Determinant line bundle} and the {\it Quillen determinant line bundle} considered on the connected component of the space of Fredholm operators including the identity operator in an intrinsic…

Using subvarieties, which we call Demazure quiver varieties, of the quiver varieties of Nakajima, we give a geometric realization of Demazure modules of Kac-Moody algebras with symmetric Cartan data. We give a natural geometric…

We generalize the results of Kahn about a correspondence between Cohen-Macaulay modules and vector bundles to non-commutative surface singularities. As an application, we give examples of non-commutative surface singularities which are not…

We introduce a Grassmannian structure for a class of quotient Hilbert modules and attack the polydisc version of Arveson-Douglas conjecture associated to distinguished varieties. More interestingly, we obtain an operator-theoretic…

A permutation is called covexillary if it avoids the pattern $3412$. We construct an open embedding of a covexillary matrix Schubert variety into a Grassmannian Schubert variety. As applications of this embedding, we show that the…

We develop a higher order generalization of the LQ decomposition and show that this decomposition plays an important role in likelihood-based estimation and testing for separable, or Kronecker structured, covariance models, such as the…

In this paper we identify the cotangent to the derived stack of representations of a quiver $Q$ with the derived moduli stack of modules over the Ginzburg dg-algebra associated with $Q$. More generally, we extend this result to finite type…

We study (a generalization of) the notion of linked determinantal loci recently introduced by the second author, showing that as with classical determinantal loci, they are Cohen-Macaulay whenever they have the expected codimension. We…

We define a family of quiver representation-valued invariants of oriented classical and virtual knots and links associated to a choice of finite quandle $X$, abelian group $A$, set of quandle 2-cocycles $C\subset H^2_Q(x;A)$, choice of…

We prove that any invariant of a 4-quiver, that is piecewise polynomial, moreover, polynomial for fixed signs of entries, is a function of determinant of a quiver.

We investigate the holonomy group of singular K\"ahler-Einstein metrics on klt varieties with numerically trivial canonical divisor. Finiteness of the number of connected components, a Bochner principle for holomorphic tensors, and a…

We study Laurent expansions of cluster variables in a cluster algebra of rank 2 associated to a generalized Kronecker quiver. In the case of the ordinary Kronecker quiver, we obtain explicit expressions for Laurent expansions of the…

We enhance the quandle coloring quiver invariant of oriented knots and links with quandle modules. This results in a two-variable polynomial invariant with specializes to the previous quandle module polynomial invariant as well as to the…

We prove two results about vector bundles on singular algebraic surfaces. First, on proper surfaces there are vector bundles of rank two with arbitrarily large second Chern number and fixed determinant. Second, on separated normal surfaces…

By combining theorems of Drinfeld and Strauch, we show that the monodromy representation on the special fibre of a Drinfeld modular variety, with level not divisible by the characteristic, is surjective. We illustrate this result in the…

Let $C$ be a simply laced generalized Cartan matrix. Given an element $b$ of the generalized braid semigroup related to $C$, we construct a collection of mutation-equivalent quivers with potentials. A quiver with potential in such a…

The goals of this article are as follows: (1) To determine the irreducible components of the affine varieties parametrizing the representations of $ \Lambda $ with dimension vector d, where $ \Lambda $ traces a major class of finite…

There are two well known tasks, related to Newton polyhedra: to study invariants of singularities in terms of their Newton polyhedra, and to describe Newton polyhedra of resultants and discriminants. We introduce so called resultantal…

We generalise the construction of fuzzy CP^N in a manner that allows us to access all noncommutative equivariant complex vector bundles over this space. We give a simplified construction of polarization tensors on S^2 that generalizes to…

We give a generic spectral decomposition of the derived category of twisted D-modules on a moduli stack of mirabolic vector bundles on a curve X in characteristic p: that is, we construct an equivalence with the derived category of…