Related papers: Moduli of McKay quiver representations II: Groebne…

We study commutative Cohen-Macaulay rings whose Cohen-Macaulay representation theory are controlled by representations of quivers, which we call hereditary representation type. Based on tilting theory and cluster tilting theory, we…

We give a moduli-theoretic proof of the classical theorem of Gabriel, stating that a scheme can be reconstructed from the abelian category of quasi-coherent sheaves over it. The methods employed are elementary and allow us to extend the…

Let $\mc G$ be a reductive group over an algebraically closed field of characteristic $p>0$. We study homogeneous $\mc G$-spaces that are induced from the $G\times G$-space $G$, $G$ a suitable reductive group, along a parabolic subgroup of…

We formulate a mathematical setup for computational neural networks using noncommutative algebras and near-rings, in motivation of quantum automata. We study the moduli space of the corresponding framed quiver representations, and find…

We calculate certain homotopy groups of the moduli spaces for representations of a compact oriented surface in the Lie groups GL(n,C) and U(p,q). Our approach relies on the interpretation of these representations in terms of Higgs bundles…

We use the framework of Quot schemes to give a novel description of the moduli spaces of stable n-pairs, also interpreted as gauged vortices on a closed Riemann surface with target Mat(r x n, C), where n >= r. We then show that these moduli…

This paper deals with sufficiency conditions for irreducibility of certain induced modules. We also construct irreducible representations for a group $G$ over a field ${\mathbb K}$ where the group $G$ is a semidirect product of a normal…

We compute explicit rational models for some Hilbert modular surfaces corresponding to square discriminants, by connecting them to moduli spaces of elliptic K3 surfaces. Since they parametrize decomposable principally polarized abelian…

In this paper, we construct the moduli spaces of filtered $G$-local systems on curves for an arbitrary reductive group $G$ over an algebraically closed field of characteristic zero. This provides an algebraic construction for the Betti…

In this paper we identify the cotangent to the derived stack of representations of a quiver $Q$ with the derived moduli stack of modules over the Ginzburg dg-algebra associated with $Q$. More generally, we extend this result to finite type…

Let $C$ be a smooth curve. In this paper we investigate the geometric properties of the double nested Hilbert scheme of points on $C$, a moduli space introduced by the third author in the context of BPS invariants of local curves and sheaf…

We study the irregularity of hypergeometric D-modules $\mathcal{M}_A (\beta )$ via the explicit construction of Gevrey series solutions along coordinate subspaces in $X =\mathbb{C}^n$. As a consequence, we prove that along coordinate…

We show a few basic results about moduli spaces of semistable modules over Lie algebroids. The first result shows that such moduli spaces exist for relative projective morphisms of noetherian schemes, removing some earlier constraints. The…

We consider the ring of coinvariants for modular representations of cyclic groups of prime order. For all cases for which explicit generators for the ring of invariants are known, we give a reduced Gr\"obner basis for the Hilbert ideal and…

Hodge classes on the moduli space of admissible covers with monodromy group G are associated to irreducible representations of G. We evaluate all linear Hodge integrals over moduli spaces of admissible covers with abelian monodromy in terms…

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…

Let $\Gamma$ be a finite group acting linearly on $\C^n$, freely outside the origin, and let $N$ be the number of conjugacy classes of $\Gamma$ minus one. A construction of Kronheimer of moduli spaces $X_\zeta$ of translation-invariant…

Let $G$ be a nontrivial finite subgroup of $\SL_n(\C)$. Suppose that the quotient singularity $\C^n/G$ has a crepant resolution $\pi\colon X\to \C^n/G$ (i.e. $K_X = \shfO_X$). There is a slightly imprecise conjecture, called the McKay…

In this paper, we give a construction of the moduli space of filtered representations of a given quiver of fixed dimension vector with the appropriate notion of stability. The construction of the moduli of filtered representations uses the…

We develop a framework to construct geometric representations of finite groups $G$ through the correspondence between real toric spaces $X^{\mathbb R}$ and simplicial complexes with characteristic matrices. We give a combinatorial…