Related papers: Lecture Notes on Quiver Representations and Moduli…

This is an expository article on the theory of algebraic stacks. After introducing the general theory, we concentrate in the example of the moduli stack of vector budles, giving a detailed comparison with the moduli scheme obtained via…

We study birational maps among 1) the moduli space of semistable torsion sheaves of Hilbert polynomial $4m+2$ on a smooth quadric surface, 2) the moduli space of semistable torsion sheaves of Hilbert polynomial $m^{2}+3m+2$ on…

Recently we suggested a new quantum algebra, the moduli algebra, which was conjectured to be a quantum algebra of observables of the Hamiltonian Chern Simons theory. This algebra provides the quantization of the algebra of functions on the…

We introduce a derived representation scheme associated with a quiver, which may be thought of as a derived version of a Nakajima variety. We exhibit an explicit model for the derived representation scheme as a Koszul complex and by doing…

We introduce the notion of a super-representation of a quiver. For super-representations of quivers over a field of characteristic zero, we describe the corresponding (super)algebras of polynomial semi-invariants and polynomial invariants.

The fixed point set under a natural torus action on projectivized moduli spaces of simple representations of quivers is described. As an application, the Euler characteristic of these moduli is computed.

This is a graduate-level introduction to C*-algebras, Hilbert C*-modules, vector bundles, and induced representations of groups and C*-algebras, with applications to quantization theory, phase space localization, and configuration space…

We construct (in significant generality) moduli spaces representing the functor of morphisms from a scheme into a solvable algebraic group.

In this paper, we consider the versal deformations of three dimensional Lie algebras. We classify Lie algebras and study their deformations by using linear algebra techniques to study the cohomology. We will focus on how the deformations…

This paper surveys some applications of moduli theory to issues concerning the distribution of rational points on algebraic varieties. It will appear on the proceedings of the Fano Conference.

The aim of this note is to outline the structure of the category of the Gorenstein projective modules for a Nakayama algebra. We are going to introduce the resolution quiver of such an algebra. It provides a fast algorithm in order to…

Torus fixed points of quiver moduli spaces are given by stable representations of the universal (abelian) covering quiver. As far as the Kronecker quiver is concerned they can be described by stable representations of certain bipartite…

We decompose each moduli space of semistable sheaves on the complex projective plane with support of dimension one and degree four into locally closed subvarieties, each subvariety being the good or geometric quotient of a set of morphisms…

We discuss selected topics on the topology of moduli spaces of curves and maps, emphasizing their relation with Gromov--Witten theory and integrable systems.

We study de Rham character sheaves on a commutative connected algebraic group $G$, defined as multiplicative line bundles with integrable connection. We construct a group algebraic space $G^\flat$ representing their moduli problem on…

This article gives an introduction for mathematicians interested in numerical computations in algebraic geometry and number theory to some recent progress in algorithmic number theory, emphasising the key role of approximate computations…

In this article, we solve the problem of constructing moduli spaces of semistable principal bundles (and singular versions of them) over smooth projective varieties over algebraically closed ground fields of positive characteristic.

This overview paper reviews several results relating the representation theory of quivers to algebraic geometry and quantum group theory. (Potential) applications to the study of the representation theory of wild quivers are discussed. To…

An introductory overview of vector spaces, algebras, and linear geometries over an arbitrary commutative field is given. Quotient spaces are emphasized and used in constructing the exterior and the symmetric algebras of a vector space.…

Motivated by applications in moduli theory, we introduce a flexible and powerful language for expressing lower bounds on relative dimension of morphisms of schemes, and more generally of algebraic stacks. We show that the theory is robust…