Related papers: Moduli Spaces of PU(2)-Instantons on Minimal Class…

Let $\mathcal{M}$ be a moduli space of polystable rank 2-bundles bundles with fixed determinant (a moduli space of $\mathrm{PU}(2)$-instantons) on a Gauduchon surface with $p_g=0$ and $b_1=1$. We study the holomorphic structure of…

In this paper, we study the moduli spaces $\mathcal{M}_{\delta,c_2}$ of stable rank-2 vector bundles on non-K\" ahler elliptic surfaces, thus giving a classification these bundles; in the case of Hopf and Kodaira surfaces, these moduli…

We develop a general strategy, based on gauge theoretical methods, to prove existence of curves on class VII surfaces. We prove that, for $b_2=2$, every minimal class VII surface has a cycle of rational curves hence, by a result of…

In this paper we describe logarithmic moduli spaces of pairs (S,D) consisting of minimal surfaces S of class VII with positive second Betti number b_2 together with reduced divisors D of b_2 rational curves. The special case of Enoki…

We give a complete description of the two-dimensional moduli spaces of stable Higgs bundles of rank 2 over complex projective line with one irregular singular point, having a regular leading-order term, and endowed with a generic compatible…

Let $S \subset \mathbb P^3$ be a very general sextic surface over complex numbers. Let $\mathcal{M}(H, c_2)$ be the moduli space of rank $2$ stable bundles on $S$ with fixed first Chern class $H$ and second Chern class $c_2$. In this…

We study the following question: Let $(X,g)$ be a compact Gauduchon surface, $(E,h)$ be a differentiable rank $r$ vector bundle on $X$, ${\mathcal{D}}$ be a fixed holomorphic structure on $D:=\det(E)$ and $a$ be the Chern connection of the…

A holomorphic triple over a compact Riemann surface consists of two holomorphic vector bundles and a holomorphic map between them. After fixing the topological types of the bundles and a real parameter, there exist moduli spaces of stable…

The compactification $\overline M_{1,3}$ of the Gieseker moduli space of surfaces of general type with $K_X^2 =1 $ and $\chi(X)=3$ in the moduli space of stable surfaces parametrises so-called stable I-surfaces. We classify all such…

We study the moduli space of minimal surfaces of general type with $K_S^2 = 1$ and $p_g = 2$ and show that it is irreducible, has dimension $28$ and admits a compactification which is unirational.

We study moduli spaces of sheaves over non-projective K3 surfaces. More precisely, if $v=(r,\xi,a)$ is a Mukai vector on a K3 surface $S$ with $r$ prime to $\xi$ and $\omega$ is a "generic" K\"ahler class on $S$, we show that the moduli…

We construct the moduli space of Spin(7)-instantons on a hermitian complex vector bundle over a closed 8-dimensional manifold endowed with a (possibly non-integrable) Spin(7)-structure. We find suitable perturbations that achieve regularity…

We study the irreducible components of the moduli space of instanton sheaves on $\mathbb{P}^3$, that is rank 2 torsion free sheaves $E$ with $c_1(E)=c_3(E)=0$ satisfying $h^1(E(-2))=h^2(E(-2))=0$. In particular, we classify all instanton…

The moduli space of instantons on an ALE space is studied using the moduli space of $\mathcal{N}=4$ field theories in three dimensions. For instantons in a simple gauge group $G$ on $\mathbb{C}^2/\mathbb{Z}_n$, the Hilbert series of such an…

It has been observed, by S. Rayan, that the complex projective surfaces that potentially admit non-trivial examples of semistable co-Higgs bundles must be found at the lower end of the Enriques-Kodaira classification. Motivated by this…

In this paper, the moduli space of singular unitary Hermitian--Einstein monopoles on the product of a circle and a Riemann surface is shown to correspond to a moduli space of stable pairs on the Riemann surface. These pairs consist of a…

A compact topological surface S, possibly non-orientable and with non-empty boundary, always admits a Klein surface structure (an atlas whose transition maps are dianalytic). Its complex cover is, by definition, a compact Riemann surface M…

We study certain moduli spaces of stable vector bundles of rank two on cubic and quartic threefolds. In many cases under consideration, it turns out that the moduli space is complete and irreducible and a general member has vanishing…

In this paper, we show the moduli spaces of stable sheaves on K3 surfaces are irreducible symplectic manifolds, if the associated Mukai vectors are primitive. More precisely, we show that they are related to the Hilbert scheme of points. We…

We give necessary conditions on complete embedded \cmc surfaces with three or four ends subject to reflection symmetries. The respective submoduli spaces are two-dimensional varieties in the moduli spaces of general \cmc surfaces. We…