Related papers: On Euler characteristics for large Kronecker quive…
Let A be the path algebra of a quiver Q with no oriented cycle. We study geometric properties of the Grassmannians of submodules of a given A-module M. In particular, we obtain some sufficient conditions for smoothness, polynomial…
In this paper we introduce and study the Euler characteristic associated with algebraic modules generated by arbitrary elements of certain noncommutative polyballs. We provide several asymptotic formulas and prove some of its basic…
This is a survey of our recent results on the geometry of moduli spaces and Teichmuller spaces of Riemann surfaces appeared in math.DG/0403068 and math.DG/0409220. We introduce new metrics on the moduli and the Teichmuller spaces of Riemann…
We show that the moduli space M(r,c) of semistable sheaves on n-dimensional projective space with support of dimension one, with multiplicity r and with Euler characteristic c is isomorphic to M(r,-c).
The geometry of the moduli space of stable spin curves is studied, with emphasis on its combinatorial properties. In this context, the standard graph theoretic framework is not just a book-keeping device: some purely combinatorial results…
Framed quiver moduli parametrize stable pairs consisting of a quiver representation and a map to a fixed graded vector space. Geometric properties and explicit realizations of framed quiver moduli for quivers without oriented cycles are…
We study the bounded derived category $\mathcal{D}$ of an Euclidean quiver, or equivalently, that of coherent sheaves on a tame weighted projective line. We give a description of the moduli space $\mathrm{ToSS}$ of the total semi-stability…
The moduli space of rank $n$ graphs, the outer automorphism group of the free group of rank $n$ and Kontsevich's Lie graph complex have the same rational cohomology. We show that the associated Euler characteristic grows like…
We associate a moduli problem to a colored trivalent graph; such graphs, when planar, appear in the state-sum description of the quantum sl(N) knot polynomial due to Murakami, Ohtsuki, and Yamada. We discuss how the resulting moduli space…
We show how quiver representations and their invariant theory natu- rally arise in the study of some moduli spaces parametrizing bundles dened on an algebraic curve, and how they lead to ne results regarding the geometry of these spaces.
For any connected component $H_0$ of the space of real meromorphic functions we build a compactification $N(H_0)$ of the space $H_0$. Then we express the Euler characteristics of the spaces $H_0$ and $N(H_0)$ in terms of topological…
We shall study moduli spaces of stable 1-dimensional sheaves on an elliptic ruled surface.
For the moduli spaces of Abelian differentials, the Euler characteristic is one of the most basic intrinsic topological invariants. We give a formula for the Euler characteristic that relies on intersection theory on the smooth…
We provide a technique to compute the Euler characteristic of a class of projective varieties called quiver Grassmannians. This technique applies to quiver Grassmannians associated with "orientable string modules". As an application we…
In this paper, we study some properties of Euler polynomials arising from umbral calculus. Finally, we give some interesting identities of Euler polynomials using our results. Recently, Dere and Simsek have studied umbral calculus related…
If a real value invariant of compact combinatorial manifolds (with or without boundary) depends only on the number of simplices in each dimension on the manifold, then the invariant is completely determined by Euler characteristics of the…
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…
We extend the scope of a former paper to vector bundle problems involving more than one vector bundle. As the main application, we obtain the solution of the well-known moduli problems of vector bundles associated with general quivers.
We give explicit computations of the $\Gamma$-Euler characteristic of several families of orbit space definable translation groupoids. These include the translation groupoids associated to finite-dimensional linear representations of the…
In this paper, we consider a generalization of the McKay correspondence in positive characteristic regarding the Euler characteristic of crepant resolutions of quotient singularities given by finite subgroups of the special linear group. As…