Bellamy, Gwyn Schedler, Travis
Published in
Selecta Mathematica

In this article, we consider Nakajima quiver varieties from the point of view of symplectic algebraic geometry. We prove that they are all symplectic singularities in the sense of Beauville and completely classify which admit symplectic resolutions. Moreover we show that the smooth locus coincides with the locus of canonically θ\documentclass[12pt]...

McGerty, Kevin Nevins, Thomas
Published in
Selecta Mathematica

To a quiver Q and choices of nonzero scalars qi\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q_i$$\end{document}, non-negative integers αi\documentclass[12pt]{minimal...

Szántó, Csaba Szöllősi, István
Published in
Acta Universitatis Sapientiae, Mathematica

Let k be an arbitrary field and Q a tame quiver of type ˜D4. Consider the path algebra kQ and the category of finite dimensional right modules mod-kQ. We determine the Hall polynomials Fxyz associated to indecomposable modules of defect ∂z =−2, ∂x = ∂y =−1 or dually ∂z = 2, ∂x = ∂y = 1.

Enomoto, Masatoshi Watatani, Yasuo
Published in
Advances in Operator Theory

We study two subspace systems in a separable infinite-dimensional Hilbert space up to (bounded) isomorphism. One of the main result of this paper is the following: Isomorphism classes of two subspace systems given by graphs of bounded operators are determined by unitarily equivalent classes of the operator ranges and the nullity of the original bou...

Das, Pradeep
Published in
Indian Journal of Pure and Applied Mathematics

This paper describes the construction of a natural Hermitian holomorphic line bundle on the stratified moduli space of complex representations of a finite quiver, which are semistable with respect to a fixed rational weight and have a fixed type. It is shown that the curvature of this Hermitian line bundle on each stratum of the moduli space is ess...

Mizuno, Yuya Thomas, Hugh
Published in
Selecta Mathematica

We give an interpretation of the map πc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi ^c$$\end{document} defined by Reading, which is a map from the elements of a ...

Andritsch, Lukas

We consider GL$_m$-dimers of triangulations of regular convex $n$-gons, which give rise to a dimer model with boundary $Q$ and a dimer algebra $\Lambda_Q$. Let $e_b$ be the sum of the idempotents of all the boundary vertices, and $\mathcal{B}_Q:= e_b \Lambda_Q e_b$ the associated boundary algebra. In this article we show that given two different tr...

Guo, Peng Zhang, Pu
Published in
Acta Mathematica Sinica, English Series

An exceptional n-cycle in a Horn-finite triangulated category with Serre functor has been recently introduced by Broomhead, Pauksztello and Ploog. When n = 1, it is a spherical object. We explicitly determine all the exceptional cycles in the bounded derived category Db (kQ) of a finite quiver Q without oriented cycles. In particular, if Q is an Eu...

Allegretti, Dylan G. L.
Published in
Selecta Mathematica

We consider a cluster variety associated to a triangulated surface without punctures. The algebra of regular functions on this cluster variety possesses a canonical vector space basis parametrized by certain measured laminations on the surface. To each lamination, we associate a graded vector space, and we prove that the graded dimension of this ve...

Ramos, Eric White, Graham
Published in
Selecta Mathematica

For fixed positive integers n and k, the Kneser graph KGn,k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$KG_{n,k}$$\end{document} has vertices labeled by k-element su...