Related papers: Quivers of sections on toric orbifolds

In this paper, we give an expository account of the geometric properties of the moduli stack of $G$-bundles. For $G$ an algebraic group over a base field and $X \to S$ a flat, finitely presented, projective morphism of schemes, we give a…

We study equivariant sheaves over profinite spaces, where the group is also taken to be profinite. We resolve a serious deficit in the existing theory by constructing a good notion of equivariant presheaves, with a suitable equivariant…

We generalize the notion of S-equivalence, previously defined for semistable vector bundles, to points in arbitrary algebraic stacks and use it to describe the identification of points when passing to the moduli space. As applications, we…

Let $G$ be a semisimple, simply connected, affine algebraic group defined over $\mathbb C$. Consider the Liouville symplectic structure on the total space $T^*G((t))$ of the cotangent bundle of the loop group $G((t))$, where $t$ is a formal…

Generalizing the classical theorems of Max Noether and Petri, we describe generators and relations for the canonical ring of a stacky curve, including an explicit Gr\"obner basis. We work in a general algebro-geometric context and treat log…

In this article we prove, in a simple way, that for any complete toric variety, and for any Cartier divisor, the ring of global sections of multiples of the line bundle associated to the divisor is finitely generated.

We work through, in detail, the orbifold quantum cohomology, with gravitational descendants, of the stack BG, the point modulo trivial action of a finite group G. We provide a simple description of algebraic structures on the state space of…

We prove a closed formula counting semistable twisted (or meromorphic) Higgs bundles of fixed rank and degree over a smooth projective curve of genus g, defined over a finite field, when the degree of the twisting line bundle is at least…

In this paper we discuss Bagger-Witten line bundles over moduli spaces of SCFTs. We review how in general they are `fractional' line bundles, not honest line bundles, twisted on triple overlaps. We discuss the special case of moduli spaces…

We introduce the notion of a Nakajima bundle representation. Given a labelled quiver and a variety or manifold $X$, such a representation involves an assignment of a complex vector bundle on $X$ to each node of the doubled quiver; to the…

Toroidal 3-orbifolds $(S^1)^6/G$, for $G$ a finite group, were some of the earliest examples of Calabi-Yau 3-orbifolds to be studied in string theory. While much mathematical progress towards the predictions of string theory has been made…

Let X be a smooth complete complex toric variety such that the boundary is a simple normal crossing divisor, and let E be a holomorphic vector bundle on X. We prove that E admits an equivariant structure if and only if E admits a…

We construct full strong exceptional collections of line bundles on smooth toric Fano Deligne-Mumford stacks of Picard number at most two and of any Picard number in dimension two. It is hoped that the approach of this paper will eventually…

In this paper I present a new geometric approach to the factorization rule for generalised theta functions. Let $X$ be an irreducible projective nodal curve with one singularity and let $Y$ be its normalization. Recently I have constructed…

Let G be a compact Lie group. We build a tower of G-spectra over the suspension spectrum of the space of linear isometries from one G-representation to another. The stable cofibres of the maps running down the tower are certain interesting…

We construct new compactifications with good properties of moduli spaces of maps from nonsingular marked curves to a large class of GIT quotients. This generalizes from a unified perspective many particular examples considered earlier in…

We start with a small paradigm shift about group representations, namely the observation that restriction to a subgroup can be understood as an extension-of-scalars. We deduce that, given a group $G$, the derived and the stable categories…

Let $G$ be a reductive group acting on an affine scheme $V$. We study the set of principal $G$-bundles on a smooth projective curve $\mathcal C$ such that the associated $V$-bundle admits a section sending the generic point of $\mathcal C$…

We consider a class of tautological top intersection products on the moduli space of stable pairs consisting of semistable vector bundles together with N sections on a smooth complex projective curve C. We show that when N is large, these…

Given a generically smooth stable curve over a discrete valuation ring such that its special fibre is irreducible with one double point, we construct a moduli stack over that descrete valuation ring which is a model for the moduli stack of…