Related papers: Moduli of quiver representations for exceptional c…

Suppose $P^n_m$ is the blow up of $\mathbb{P}^n$ at a linear subspace of dimension $m$, $\mathcal{L}=\{L_1,\ldots,L_r\}$ is a (not necessarily full) strong exceptional collection of line bundles on $P^n_m$. Let $Q$ be the quiver associated…

We study exceptional collections of line bundles on surfaces. We prove that any full cyclic strong exceptional collection of line bundles on a rational surface is an augmentation in the sense of L.Hille and M.Perling. We find simple…

We study full exceptional collections of line bundles on surfaces. We prove that any full strong exceptional collection of line bundles on a weak del Pezzo surface of degree $\ge 3$ is an augmentation in the sense of L.Hille and M.Perling,…

We construct Mori Dream Spaces as fine moduli spaces of representations of bound quivers, thereby extending results of Craw--Smith \cite{CrawSmith} beyond the toric case. Any collection of effective line bundles $\mathscr{L}=(\mathscr{O}_X,…

We prove that any numerically exceptional collection of maximal length, consisting of line bundles, on a smooth del Pezzo surface is a standard augmentation in the sense of L.Hille and M.Perling. We deduce that any such collection is…

For any moduli space of stable representations of quivers, certain smooth varieties, compactifying projective space fibrations over the moduli space, are constructed. The boundary of this compactification is analyzed. Explicit formulas for…

We prove that, for a natural class of Bridgeland stability conditions on $\mathbb{P}^1\times\mathbb{P}^1$ and the blow-up of $\mathbb{P}^2$ at a point, the moduli spaces of Bridgeland semistable objects are projective. Our technique is to…

We use categorical method and birational geometry to study moduli spaces of quiver representations. From certain "representable" functor, we construct a birational transformation from the moduli space of representations of one quiver to…

In this paper, we study certain moduli spaces of vector bundles on the blowup of the projective plane in at least 10 very general points. Moduli spaces of sheaves on general type surfaces may be nonreduced, reducible and even disconnected.…

This is a review article exploring similarities between moduli of quiver representations and moduli of vector bundles over a smooth projective curve. After describing the basic properties of these moduli problems and constructions of their…

We consider the fine quiver moduli space of representations of the 3-Kronecker quiver of dimension vector $(2,3)$, which is a blow down of the Hilbert scheme of 3 points on $\mathds{P}^2$. A short description of its geometry and Chow ring…

We give a moduli-theoretic treatment of the existence and properties of moduli spaces of semistable quiver representations, avoiding methods from geometric invariant theory. Using the existence criteria of Alper--Halpern-Leistner--Heinloth,…

We examine the moduli of framed holomorphic bundles over the blowup of a complex surface, by studying a filtration induced by the behavior of the bundles on a neighborhood of the exceptional divisor.

We study the principal parts bundles $P^k (L)$ of the degree $d$ line bundle $L$ on the $n$ dimensional projective space as homogeneous bundles and we describe their associated quiver representations. We use this approach to show that if…

We prove the irreducibility of the moduli space of rank 2 semistable torsion free sheaves (with a generic polarization and any value of c_2) on a K3 or a del Pezzo surface. In the case of a K3 surface, we need to prove a result on the…

This article describes some complex-analytic aspects of the moduli space of the finite-dimensional complex representations of a finite quiver, which are stable with respect to a fixed rational weight. We construct a natural structure of a…

This is the first of two papers studying moduli spaces of a certain class of coherent sheaves, which we call {\it stable perverse coherent sheaves}, on the blowup of a projective surface. They are used to relate usual moduli spaces of…

This paper proves that every projective toric variety is the fine moduli space for stable representations of an appropriate bound quiver. To accomplish this, we study the quiver $Q$ with relations $R$ corresponding to the finite-dimensional…

The new compactification of moduli scheme of Gieseker-stable vector bundles with the given Hilbert polynomial on a smooth projective polarized surface (S;H), over the field k = \bar k of zero characteristic, is constructed in previous…

A conjecture of Bondal-Polishchuk states that, in particular for the bounded derived category of coherent sheaves on a smooth projective variety, the action of the braid group on full exceptional collections is transitive up to shifts. We…