Related papers: Twisted bundles and admissible covers

For a stable irreducible curve $X$ and a torsion free sheaf $L$ on $X$ of rank one and degree $d$, D.S. Nagaraj and C.S. Seshadri ([NS]) defined a closed subset $\Cal U_X(r,L)$ in the moduli space of semistable torsion free sheaves of rank…

Fix a smooth projective curve over a field of characteristic zero and a finite set of punctures. Let G be a connected linear algebraic group. We prove that the moduli of G-bundles with logarithmic connections having fixed residue classes at…

We prove that any flat G-bundle, where G is a complex connected reductive algebraic group, on the punctured disc admits the structure of an oper. This result is important in the local geometric Langlands correspondence proposed in…

In this paper, which is a sequel of arXiv:2002.07494, we investigate, for any reductive group $G$ over an algebraically closed field $k$, the Picard group of the universal moduli stack $\mathrm{Bun}_{G,g,n}$ of $G$-bundles over $n$-pointed…

Given any irreducible smooth complex projective curve $X$, of genus at least $2$, consider the moduli stack of vector bundles on $X$ of fixed rank and determinant. It is proved that the isomorphism class of the stack uniquely determines the…

We give an algebro-geometric derivation of the known intersection theory on the moduli space of stable rank 2 bundles of odd degree over a smooth curve of genus g. We lift the computation from the moduli space to a Quot scheme, where we…

We study a family of canonically polarized surfaces introduced by Persson, which arise as Galois $G=(\mathbb{Z}/2\mathbb{Z})^4$-covers of $\mathbf{P}^2$ branched along eight general lines. For this family, we construct the compactified…

Given a connected reductive algebraic group G, we investigate the Picard group of the moduli stack of principal G-bundles over an arbitrary family of smooth curves.

We use the theory of twisted stable maps to Deligne-Mumford stacks to construct compactifications of the moduli space of pairs $(X \to C, S + F)$ where $X \to C$ is a fibered surface, $S$ is a sum of sections, $F$ is a sum of marked fibers,…

The moduli stack of Deligne-Mumford stable curves of genus g admits a stratification, so that the number of nodes of the curves belonging to one stratum is constant. The irreducible components of the stratum corresponding to curves with…

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…

Let $R$ be a complete discrete valuation ring with fraction field of characteristic $0$ and algebraically closed residue field of characteristic $p>0$. Let $X_R \to \mathrm{Spec}(R)$ be a smooth projective morphism of relative dimension…

In this note we prove a new explicit formula for the invariants of moduli spaces of twisted Higgs bundles over P^1 and we relate these invariants to the invariants of moduli spaces of representations of some infinite symmetric quiver. The…

Let G be a split reductive group. We introduce the moduli problem of "bundle chains" parametrizing framed principal G-bundles on chains of lines. Any fan supported in a Weyl chamber determines a stability condition on bundle chains. Its…

In this paper, we explore the theme of orbifold stratified spaces and establish a general criterion for them to be smooth orbifolds. This criterion utilizes the notion of linear stratification on the gluing bundles for the orbifold…

We construct the moduli space for equivalence classes of n-pointed tropical curves of genus g, together with its compactification given by weighted tropical curves, and establish some of its basic topological properties. We compare it to…

Consider genus g curves that admit degree d covers to an elliptic curve simply branched at 2g-2 points. Vary a branch point and the locus of such covers forms a one-parameter family W. We investigate the geometry of W by using admissible…

Let $Y$ denote an irreducible projective curve with at most nodes as singularities and defined over an algebraically closed field of characteristic zero. We study the restriction of the twisted Picard bundles on the compactified Jacobian…

There is a well-known stratification of the moduli space $M_g$ of Deligne-Mumford stable curves of genus $g$ by the loci of stable curves with a fixed number $i$ of nodes, where $i \le 3g-3$. The associated moduli stack ${\cal M}_g$ admits…

We study Hodge Integrals on Moduli Spaces of Admissible Covers. Motivation for this work comes from Bryan and Pandharipande's recent work on the local GW theory of curves, where analogouos intersection numbers, computed on Moduli Spaces of…