Related papers: A note on monopole moduli spaces

Consider the $3$-dimensional $\mathcal N=4$ supersymmetric gauge theory associated with a compact Lie group $G$ and its quaternionic representation $\mathbf M$. Physicists study its Coulomb branch, which is a noncompact hyper-K\"ahler…

We study framed translation surfaces corresponding to meromorphic differentials on compact Riemann surfaces, for which a horizontal separatrix is marked for each pole or zero. Such geometric structures naturally appear when studying flat…

Let $\cM_{g,n}$ be the moduli space of Riemann surfaces of genus $g$ with $n$ punctures. From a complex perspective, moduli space is hyperbolic. For example, $\cM_{g,n}$ is abundantly populated by immersed holomorphic disks of constant…

Let X be a smooth irreducible complex projective curve of genus g > 1. In this paper, we give necessary and sufficient conditions for an unstable bundle of HN-lenght 2 to have a particular algebra of endomorphisms. Then, fixing the…

The moduli space metric for an arbitrary number of extremal black holes in four dimensions with arbitrary relatively supersymmetric charges is found.

This paper is a sequel to [He7]. There a notion of marking of isolated hypersurface singularities was defined, and a moduli space $M_\mu^{mar}$ for marked singularities in one $\mu$-homotopy class of isolated hypersurface singularities was…

Let $(X,g)$ be a compact Riemannian stratified space with simple edge singularity. Thus a neighbourhood of the singular stratum is a bundle of truncated cones over a lower dimensional compact smooth manifold. We calculate the various…

The known counterexamples to the global Torelli theorem for higher-dimensional hyperkahler manifolds are provided by birational manifolds. We address the question whether two birational hyperkahler manifolds (i.e. irreducible symplectic)…

For every $k \geq 2$ we construct infinitely many $4k$-dimensional manifolds that are all stably diffeomorphic but pairwise not homotopy equivalent. Each of these manifolds has hyperbolic intersection form and is stably parallelisable. In…

We show how in the presence of RR two-form field strength the conditions for preserving supersymmetry on six- and seven-dimensional manifolds lead to certain generalizations of monopole equations. For six dimensions the string frame metric…

The space of unitary local systems of rank one on the complement of an arbitrary divisor in a complex projective algebraic variety can be described in terms of parabolic line bundles. We show that multiplier ideals provide natural…

On a symplectic manifold $(M, \omega)$, a spacefilling brane structure is a closed 2-form $F$ which determines a complex structure, with respect to which $F +i\omega$ is holomorphic symplectic. For holomorphic symplectic compact K\"ahler…

The low velocity dynamic of a doubly periodic monopole, also called a monopole wall or monowall for short, is described by geodesic motion on its moduli space. This moduli space is hyperkaehler and non-compact. We establish a relation…

Apart from global topological problems an affine homogeneous space is locally described by its curvature, its torsion and a slightly less tangible object called its connection in a given base point. Using this description of the local…

Complete, conformally flat metrics of constant positive scalar curvature on the complement of $k$ points in the $n$-sphere, $k \ge 2$, $n \ge 3$, were constructed by R\. Schoen [S2]. We consider the problem of determining the moduli space…

This is the addendum to the paper "On the Multiplicity Problem and the Isomorphism Problem for the Four Subspace Algebra" Communications in Algebra, 40:6 (2012), 2005-2036 (DOI: 10.1080/00927872.2011.570830). We give here the full proof of…

Harmonic maps that minimise the Dirichlet energy in their homotopy classes are known as lumps. Lump solutions on real projective space are explicitly given by rational maps subject to a certain symmetry requirement. This has consequences…

We propose a universal expression for the moduli metric of a class of four- and five-dimensional black holes which preserve at least four supersymmetries. These include the black holes that are associated with various intersecting branes in…

In this paper we determine the moduli space, up to isometric automorphism, of left-invariant metrics on a $6$-dimensional Lie group $H$, such that its Lie algebra $\mathfrak{h}$ admits a complex structure and has first Betti number equal to…

This paper is a review of current developments in the study of moduli spaces of G2 manifolds. G2 manifolds are 7-dimensional manifolds with the exceptional holonomy group G2. Although they are odd-dimensional, in many ways they can be…