相关论文: A correspondence between rigid modules over path a…

We start with observing that the only connected finite dimensional algebras with finitely many isomorphism classes of indecomposable bimodules are the quotients of the path algebras of uniformly oriented $A_n$-quivers modulo the radical…

In this paper we study equivariant moduli spaces of sheaves on a $ K3 $ surface $ X $ under a symplectic action of a finite group. We prove that under some mild conditions, equivariant moduli spaces of sheaves on $ X $ are irreducible…

We prove that on a nonsingular quadric hypersurface Q in $P^4_k$ even CI liaison classes of ACM curves are in bijective correspondence with the stable equivalence classes (up to shift in degree) of maximal Cohen-Macaulay graded modules over…

We study aspects of noncommutative Riemannian geometry of the path algebra arising from the Kronecker quiver with N arrows. To start with, the framework of derivation based differential calculi is recalled together with a discussion on…

Suppose that $Q$ is a connected quiver without oriented cycles and $\sigma$ is an automorphism of $Q$. Let $k$ be an algebraically closed field whose characteristic does not divide the order of the cyclic group $\langle\sigma\rangle$. The…

In a recent paper by K.-H. Lee and K. Lee, rigid reflections are defined for any Coxeter group via non-self-intersecting curves on a Riemann surface with labeled curves. When the Coxeter group arises from an acyclic quiver, the rigid…

We explore the differential geometry of finite sets where the differential structure is given by a quiver rather than as more usual by a graph. In the finite group case we show that the data for such a differential calculus is described by…

In this paper, we describe the spectral correspondence for cyclic Higgs bundles from the viewpoint of quiver bundles. Under this framework, we establish a one-to-one correspondence between cyclic Higgs bundles on a curve and sheaves on a…

In this note, we will illuminate some immediate consequences of work done by Reineke that may prove to be useful in the study of elliptic curves. In particular, we will construct an isomorphism between the category of smooth projective…

Given two irreducible curves of the plane which have isomorphic complements, it is natural to ask whether there exists an automorphism of the plane that sends one curve on the other. This question has a positive answer for a large family of…

$Q$ is a quiver of type $\tilde A(n-1,1)$ if its graph is of affine type $\tilde A_{n-1}$ and if its arrows have a certain orientation. We develop a bijection between the set of indecomposable $kQ$-modules whose dimension vectors are…

In this paper we show that for any affine complete rational surface singularity there is a correspondence between the dual graph of the minimal resolution and the quiver of the endomorphism ring of the special CM modules. We thus call such…

We extend the Horrocks correspondence between vector bundles and cohomology modules on the projective plane to the product of two projective lines. We introduce a set of invariants for a vector bundle on the product of two projective lines,…

A general definition of a bimodule connection in noncommutative geometry has been recently proposed. For a given algebra this definition is compared with the ordinary definition of a connection on a left module over the associated…

We examine the proposal made recently that the su(3) modular invariant partition functions could be related to the geometry of the complex Fermat curves. Although a number of coincidences and similarities emerge between them and certain…

The irreducible components of varieties parametrizing the finite dimensional representations of a finite dimensional algebra $\Lambda$ are explored, with regard to both their geometry and the structure of the modules they encode. Provided…

An integral hyperbolic lattice is called reflective if its automorphism group is generated by reflections, up to finite index. Since 1981, it is known that their number is essentially finite. We show that K3 surfaces over C with reflective…

We study non-commutative projective lines over not necessarily algebraic bimodules. In particular, we give a complete description of their categories of coherent sheaves and show they are derived equivalent to certain bimodule species. This…

We consider the variant of Mirror Symmetry Conjecture for K3 surfaces which relates "geometry" of curves of a general member of a family of K3 with "algebraic functions" on the moduli of the mirror family. Lorentzian Kac--Moody algebras are…

Motivated by the problem of classifying quantum symmetries of non-semisimple, finite-dimensional associative algebras, we define a notion of connection between bounded quivers and build a bicategory of bounded quivers and quiver…