Related papers: A remarkable moduli space of rank 6 vector bundles…

In this paper, we prove that the moduli space $\overline{M}_{X}(\nu)$ of $H$-Gieseker semistable sheaves on a smooth cubic threefold $X$ with Chern character $\nu=(4,-H,-\frac{5}{6}H^{2},\frac{1}{6}H^{3})$ is non-empty, smooth and…

In this paper we investigate the moduli spaces of semistable coherent sheaves of rank two on the projective space $\mathbb{P}^3$ and the following rational Fano manifolds of the main series - the three-dimensional quadric $X_2$, the…

We generalise Fl\o{}ystad's theorem on the existence of monads on the projective space to a larger set of projective varieties. We consider a variety $X$, a line bundle $L$ on $X$, and a base-point-free linear system of sections of $L$…

In this paper, we study the moduli spaces of canonical threefolds with any prescribed geometric genus $p_g \ge 5$ which have the smallest possible canonical volume. This minimal volume is equal to the smallest half-integer that is larger…

This is a note in which we first review symmetries of moduli spaces of stable meromorphic connections on trivial vector bundles over the Riemann sphere, and next discuss symmetries of their integrable deformations as an application. In the…

We prove that the weight-two Hodge structure of moduli spaces of torsion-free sheaves on a K3 surface is as described by Mukai (the rank is arbitrary but we assume the first Chern class is primitive). We prove the moduli space is an…

Let $(X,\,D)$ be an $m$-pointed compact Riemann surface of genus at least $2$. For each $x \,\in\, D$, fix full flag and concentrated weight system $\alpha$. Let $P \mathcal{M}_{\xi}$ denote the moduli space of semi-stable parabolic vector…

The Weddle surface is classically known to be a birational (partially desingularized) model of the Kummer surface. In this note we go through its relations with moduli spaces of abelian varieties and of rank two vector bundles on a genus 2…

For a classical simple and simply connected group $G$, let $\mathcal{M}_{G,\omega}$ be the moduli space of $\omega$-semistable parabolic $G$-bundles on a complex smooth projective curve of genus $g$. We prove two results in this article:…

The goal of this paper is to construct universal cohomology classes on the moduli space of stable bundles over a curve when it is not a fine moduli space, i.e. when the rank and degree are not coprime. More precisely, we show that certain…

Let $X$ be a smooth projective curve of genus $g\geq 2$ over an algebraically closed field $k$ of characteristic $p>0$, $F_X:X\rightarrow X$ the absolute Frobenius morphism. Let $\M^s_X(r,d)$ be the moduli space of stable vector bundles of…

Moduli of vector bundles on stacky curves behave similarly to moduli of vector bundles on curves, except there are additional numerical invariants giving many different notions of stability. We apply the existence criterion for good moduli…

This paper is devoted to the study of the uniformization of the moduli space of pairs (X, E) consisting of an algebraic curve and a vector bundle on it. For this goal, we study the moduli space of 5-tuples (X, x, z, E, \phi), consisting of…

We describe new irreducible components of the moduli space of rank $2$ semistable torsion free sheaves on the three-dimensional projective space whose generic point corresponds to non-locally free sheaves whose singular locus is either…

In this paper, certain natural and elementary polygonal objects in Euclidean space, {\it the stable polygons}, are introduced, and the novel moduli spaces ${\bfmit M}_{{\bf r}, \epsilon}$ of stable polygons are constructed as complex…

Let $\mathcal M_{r,c}$ denote the moduli space of stable bundles with rank $r$ and second Chern class $c>0$ on a Hopf surface. We prove that the subset of $\mathcal M_{r,c}$ formed by irregular bundles is meager.

Representations of certain vertex algebras, here called of CohFT-type, can be used to construct vector bundles of coinvariants and conformal blocks on moduli spaces of stable curves [DGT2]. We show that such bundles define semisimple…

We classify all Gieseker semi-stable sheaves on the complex projective plane that have dimension 1, multiplicity 6 and Euler characteristic 3. We show that their moduli space is birational to the blow-up at a special point of a certain…

We describe the components of the moduli space of conjugacy classes of commuting pairs and triples of elements in a compact Lie group. This description is in terms of the extended Dynkin diagram of the simply connected cover, together with…

Let $X$ be a smooth projective curve of genus $g$ over the field $\mathbb{C}$. Let $M_{X}(2,L)$ denote the moduli space of stable rank $2$ vector bundles on $X$ with fixed determinant $L$ of degree $2g-1$. Consider the Brill-Noether…