Related papers: Stratified Obstruction Systems for Equivariant Mod…

This article is devoted to branching problems for holomorphic discrete series representations of a conformal group $G$ of a tube domain $T_Omega$ over a symmetric cone $\Omega$. More precisely, we analyse restrictions of such…

The quantization of vector bundles is defined. Examples are constructed for the well controlled case of equivariant vector bundles over compact coadjoint orbits. (Coadjoint orbits are symplectic spaces with a transitive, semisimple symmetry…

We give a complete classification of equivariant vector bundles of rank two over smooth complete toric surfaces and construct moduli spaces of such bundles. This note is a direct continuation of an earlier note where we developed a general…

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…

This is a continuation of the authors' previous work [math.AT/9910001] on classification of equivariant complex vector bundles over a circle. In this paper we classify equivariant real vector bundles over a circle with a compact Lie group…

We formulate a theory of instability and Harder-Narasimhan filtrations for an arbitrary moduli problem in algebraic geometry. We introduce the notion of a $\Theta$-stratification of a moduli problem, which generalizes the Kempf-Ness…

Let $A$ be a regular ring over a field $k$, with $1/2\in k$ and dimension $d$. We discuss the Homotopy Conjecture of Madhav V. Nori, in the complete intersection case (meaning when the projective module in question if free, of rank at least…

For the moduli spaces of Abelian differentials, the Euler characteristic is one of the most basic intrinsic topological invariants. We give a formula for the Euler characteristic that relies on intersection theory on the smooth…

Using the machinery of etale homotopy theory a' la Artin-Mazur we determine the etale homotopy types of moduli stacks over $\bar{\Q}$ parametrizing families of algebraic curves of genus g greater than 1 endowed with an action of a finite…

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…

Boij-S\"oderberg theory concerns resolutions of graded modules over a polynomial ring over a field. Specifically Boij-S\"oderberg theory gives a description of the cone of Betti diagrams for Cohen-Macaulay modules. Eisenbud and Schreyer…

Let $X$ be a connected complex manifold equipped with a holomorphic action of a complex Lie group $G$. We investigate conditions under which a principal bundle on $X$ admits a $G$--equivariance structure.

In this paper, we show a strange duality isomorphism at level one for the space of generalized theta functions on the moduli spaces of alternating anti-invariant vector bundles in the ramified case. These anti-invariant vector bundles…

Phenomenological implications of the volume of the Calabi-Yau threefolds on the hidden and observable M-theory boundaries, together with slope stability of their corresponding vector bundles, constrain the set of Kaehler moduli which give…

Heterotic string compactifications on integrable $G_2$ structure manifolds $Y$ with instanton bundles $(V,A), (TY,\tilde{\theta})$ yield supersymmetric three-dimensional vacua that are of interest in physics. In this paper, we define a…

A major problem in discussing heterotic string models is the stabilisation of the many vector bundle moduli via the superpotential generated by world-sheet instantons. In arXiv:1110.6315 we have discussed the method to make a discrete twist…

Techniques are presented for computing the cohomology of stable, holomorphic vector bundles over elliptically fibered Calabi-Yau threefolds. These cohomology groups explicitly determine the spectrum of the low energy, four-dimensional…

We use geometric invariant theory and the language of quivers to study compactifications of moduli spaces of linear dynamical systems. A general approach to this problem is presented and applied to two well known cases: We show how both…

We study smooth maps between smooth manifolds with only fold points as their singularities, and clarify the obstructions to the existence of such a map in a given homotopy class for certain dimensions. The obstructions are described in…

Let T be the one-dimensional complex torus. We consider the action of an automorphism of a Riemann surface X on the cohomology of the T-equivariant determinant line bundle over the moduli space of rank two Higgs bundles on X with fixed…