Related papers: Moduli of representations of quivers
Let $\Lambda$ be a basic finite dimensional algebra over an algebraically closed field, presented as a path algebra modulo relations; further, assume that $\Lambda$ is graded by lengths of paths. The paper addresses the classifiability, via…
In this paper, we introduce a new notion of representation for a locally convex partial *-algebraic module as a concrete space of maps. This is a continuation of our systematic study of locally convex partial *-algebraic modules, which are…
We study Euler characteristics of moduli spaces of stable representations of m-Kronecker quivers for m>>0.
We construct the moduli space for equivalence classes of n-pointed tropical curves of genus g, together with its compactification given by weighted tropical curves, and establish some of its basic topological properties. We compare it to…
In this expository article, we present a brief introduction to the theory of Hilbert modular forms and Galois representations, and describe what it means to attach a compatible system of Galois representations to a Hilbert modular form.
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 construct (in significant generality) moduli spaces representing the functor of morphisms from a scheme into a solvable algebraic group.
We contribute to the foundations of tropical geometry with a view towards formulating tropical moduli problems, and with the moduli space of curves as our main example. We propose a moduli functor for the moduli space of curves and show…
In this paper, we explore the virtual technique that is very useful in studying moduli problem from differential geometric point of view. We introduce a class of new objects "virtual manifolds/orbifolds", on which we develop the integration…
The constructions of the virtual Euler (or moduli) cycles and their properties are explained and developed systematically in the general abstract settings.
In this work, we introduce {\em topological representations of a quiver} as a system consisting of topological spaces and its relationships determined by the quiver. Such a setting gives a natural connection between topological…
The author constructs the moduli of representations whose images generate the subalgebra of upper triangular matrices (up to inner automorphisms) of the full matrix ring for any groups and any monoids.
We analyse the vector bundle moduli arising from generic heterotic compactifications from the point of view of quiver representations. Phenomena such as stability walls, crossing between chambers of supersymmetry, splitting of non-Abelian…
Moduli theory has captured the imagination of algebraic geometers for at least two centuries. Up until the end of the 20th century, moduli spaces were constructed and studied by rigidifying the moduli problem using extrinsic data and…
Multisorted modules, equivalently representations of quivers, equivalently additive functors on preadditive categories, encompass a wide variety of additive structures. In addition, every module has a natural and useful multisorted…
This survey provides an introduction to basic questions and techniques surrounding the topology of the moduli space of stable Higgs bundles on a Riemann surface. Through examples, we demonstrate how the structure of the cohomology ring of…
It is shown that rational points over finite fields of moduli spaces of stable quiver representations are counted by polynomials with integer coefficients. These polynomials are constructed recursively using an identity in the Hall algebra…
We describe the topology of the moduli spaces of flat metrics for all the 3-dimensional closed manifolds. We give an algebraic description of the moduli spaces for the 4-dimensional closed flat manifolds with a single generator in their…
In this expository note, we offer an overview of the relationship between Hodge-theoretic and geometric compactifications of moduli spaces of algebraic varieties.
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.