Related papers: Universal Hitchin moduli spaces

We study the moduli space M(G,A) of flat G-bundles on an Abelian surface A, where G is a compact, simple, simply connected, connected Lie group. Equivalently, M(G,A) is the (coarse) moduli space of s-equivalence classes of holomorphic…

We consider the moduli space MN of flat unitary connections on an open Kaehler manifold U (complement of a divisor with normal crossings) with restrictions on their monodromy transformations. Using intersection and L2 cohomologies with…

Using a geometric realization of the $SU(2)_R$ symmetry and a procedure of factorisation of the gauge and $SU(2)_R$ charges, we study the small instanton singularities of the Higgs branch of supersymmetric $U(1)^r$ gauge theories with eight…

In this manuscript, we aim to classify and characterize the moduli space of homogeneous spin connections and homogeneous SU(2) connections on three-dimensional Riemannian homogeneous spaces. An analysis of the topology of the associated…

We construct the twistor space associated with an HKT manifold, that is, a hyper-K\"ahler manifold with torsion, a type of geometry that arises as the target space geometry in two-dimensional sigma models with (4,0) supersymmetry. We show…

We prove that every Kaehler metric, whose potential is a function of the time-like distance in the flat Kaehler-Lorentz space, is of quasi-constant holomorphic sectional curvatures, satisfying certain conditions. This gives a local…

We obtain a compactness result for various classes of Riemannian metrics in dimension four; in particular our method applies to anti-self-dual metrics, Kahler metrics with constant scalar curvature, and metrics with harmonic curvature. With…

We show the smoothness over the affine line of the Hodge moduli space of logarithmic t-connections of coprime rank and degree on a smooth projective curve with geometrically integral fibers over an arbitrary Noetherian base. When the base…

In this paper, we study Hermitian-Yang-Mills connections (HYM) on a smooth Hermitian vector bundle over compact K\"{a}hler manifold. We calculate the virtual dimension of the moduli space of HYM connections and provide an analytic proof…

We define and parametrise so-called $\mathfrak{sl}(2)$-type fibres of the $\mathsf{Sp}(2n,\mathbb{C})$- and $\mathsf{SO}(2n+1,\mathbb{C})$-Hitchin system. These are (singular) Hitchin fibres, where the spectral curve induces a two-sheeted…

This is the second article in the collection of reviews "Exact results on N=2 supersymmetric gauge theories", ed. J. Teschner. The space of vacua of class $\cal S$ theories on $R^3 \times S^1$ can be identified as the moduli space of…

We prove that Hitchin's generalized Kaehler structure on the moduli space of instantons over a compact, even generalized Kaehler four-manifold may be obtained by generalized Kaehler reduction, in analogy with the usual Kaehler case. The…

In this paper we study the relation between parabolic Higgs bundles and irreducible representations of the fundamental group of punctured Riemann surfaces established by Simpson. We generalize a result of Hitchin, identifying those…

In this paper, certain natural and elementary polygonal objects in Euclidean space, {\it the stable polygons}, are introduced, and the novel moduli spaces ${\bfmit M}_{{\bf r}, \epsilon}$ of stable polygons are constructed as complex…

We study a natural functional on the space of holomorphic sections of the Deligne-Hitchin moduli space of a compact Riemann surface, generalizing the energy of equivariant harmonic maps corresponding to twistor lines. We give a link to a…

We establish an isomorphism of complex $K$-theory of the moduli space $\check{\mathcal{M}}$ of $``SL_n"$-Higgs bundles of degree $d$ and rank $n$ (in the sense of Hausel--Thaddeus) and twisted complex $K$-theory of the orbifold…

This article contains a compression of results from alg-geom/9501001, with most proofs omitted. We prove that every two points of the connected moduli space of holomorphically symplectic manifolds can be connected with so-called ``twistor…

Using global considerations, Mess proved that the moduli space of globally hyperbolic flat Lorentzian structures on $S\times\mathbb{R}$ is the tangent bundle of the Teichm\"uller space of $S$, if $S$ is a closed surface. One of the goals of…

We study the geometry of the moduli space of planes in a general cubic 5-fold and its deformation. We show that this moduli space is a smooth projective surface whose canonical bundle is ample. We also show that the variation of degree 1…

Given a holomorphic Lagrangian fibration of a compact hyperkahler manifold, we use the differential geometry of the special Kahler metric that exists on the base away from the discriminant locus, and show that the pullback of the tangent…