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]...
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...
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.
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...
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...
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 ...
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...
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...
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...
Published in Forum Mathematicum
For an interval finite quiver Q, we introduce a class of flat representations. We classify the indecomposable projective objects in the category rep ( Q ) {\mathrm{rep}(Q)} of pointwise finite dimensional representations. We show that an object in rep ( Q ) {\mathrm{rep}(Q)} is projective if and only if it is a direct sum of countably generated...
