Related papers: Vector bundles on blown-up Hopf surfaces

A general conjecture is stated on the cone of automorphic vector bundles admitting nonzero global sections on schemes endowed with a smooth, surjective morphism to a stack of $G$-zips of connected-Hodge-type; such schemes should include all…

Under some assumptions, we compute the Picard group of moduli of stable sheaves on Abelian surfaces. Considering relative moduli spaces, it is sufficient to consider the moduli of stable sheaves on the product of elliptic curves. By using…

We introduce the moduli space of marked, complete, Nielsen-convex hyperbolic structures on a surface of negative, but not necessarily finite, Euler characteristic. The emphasis is on infinite type surfaces, the aim being to study mapping…

We present a survey on the moduli spaces of rank 2 quadric bundles over a compact Riemann surface X. These are objects which generalise orthogonal bundles and which naturally occur through the study of the connected components of the moduli…

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…

We introduce three non-compact moduli stacks parametrizing noncommutative deformations of Hirzebruch surfaces; the first is the moduli stack of locally free sheaf bimodules of rank 2, which appears in the definition of noncommutative…

We construct a compactification of the moduli spaces of abelian differentials on Riemann surfaces with prescribed zeroes and poles. This compactification, called the moduli space of multi-scale differentials, is a complex orbifold with…

In this paper, we compare the moduli spaces of rank-3 vector bundles stable with respect to different ample divisors over rational ruled surfaces. We also discuss the irreducibility, unirationality, and rationality of these moduli spaces.

In this article, we solve the problem of constructing moduli spaces of semistable principal bundles (and singular versions of them) over smooth projective varieties over algebraically closed ground fields of positive characteristic.

This paper introduces $\infty$- and $n$-fold vector bundles as special functors from the $\infty$- and $n$-cube categories to the category of smooth manifolds. We study the cores and "n-pullbacks" of $n$-fold vector bundles and we prove…

In the time evolution of fluids, the topologies of fluids can be changed by the creations and annihilations of singular points and by switching combinatorial structures of separatrices. In this paper, to describe the possible generic time…

We present a method for compactifying stacks of $\PGL_n$-torsors (Azumaya algebras) on algebraic spaces. In particular, when the ambient space is a smooth projective surface we use our methods to show that various moduli spaces are…

Let M be a moduli space of stable vector bundles on a curve with rank and degree fixed and coprime. We give a simple proof that the rational cohomology of M is generated by the Kunneth components of the Chern classes of the universal…

In this paper, we construct the moduli space of marked oper structures on a closed, oriented smooth surface of negative Euler characteristic as a holomorphic fiber bundle over Teichm\"{u}ller space. We prove that the holonomy map from the…

We resolve pathological wall-crossing phenomena for moduli spaces of sheaves on higher-dimensional base manifolds. This is achieved by considering slope-semistability with respect to movable curves rather than divisors. Moreover, given a…

We give a method to construct stable vector bundles whose rank divides the degree over curves of genus bigger than one. The method complements the one given by Newstead. Finally, we make some systematic remarks and observations in…

We have studied irreducible Hom-Lie algebroid connections for Hom-bundle and prove that the H-gauge theoretic moduli space has a Hausdorff Hilbert manifold structure. This work generalizes some known results about simple semi-connections…

Following Deligne and Mumford we construct a coarse moduli space of smooth curves with non-abelian level structure, involving higher order commutators. We prove that its Deligne-Mumford compactification is smooth over an open part of…

The moduli space of slope-stable vector bundles on a normal projective variety over an algebraically closed field of characteristic $p\geq 0$ is stratified with respect to the decomposition type. On a smooth projective curve of genus at…

Given a geometrically irreducible smooth projective curve of genus 1 defined over the field of real numbers, and a pair of integers r and d, we determine the isomorphism class of the moduli space of semi-stable vector bundles of rank r and…