Related papers: The twistor transform of a Verlinde formula

The space of topological decompositions into triangulations of a surface has a natural graph structure where two triangulations share an edge if they are related by a so-called flip. This space is a sort of combinatorial Teichm\"uller space…

We extend Teichmueller dynamics to a flow on the total space of a flat bundle of deformation spaces of representations of the fundamental group of a fixed surface S in a Lie group G. The resulting dynamical system is a continuous version of…

Triangulated surfaces are compact Riemann surfaces equipped with a conformal triangulation by equilateral triangles. In 2004, Brooks and Makover asked how triangulated surfaces are distributed in the moduli space of Riemann surfaces as the…

We establish an isomorphism between the moduli space of homologically trivial parabolic (Higgs) bundles on $\mathbb{P}^1$ and the quiver variety associated to a star-shaped quiver. As applications, we deduce a closed formula for the…

We prove an analog of the Verlinde formula on the moduli space of semistable meromorphic G-Higgs bundles over a smooth curve for a reductive group G whose fundamental group is free. The formula expresses the graded dimension of the space of…

We show that the moduli space $M$ of holomorphic vector bundles on $CP^3$ that are trivial along a line is isomorphic (as a complex manifold) to a subvariety in the moduli of rational curves of the twistor space of the moduli space of…

We study rank-one sheaves and stable pairs on a smooth projective complex surface. We obtain an embedding of the moduli space of limit stable pairs into a smooth space. The embedding induces a perfect obstruction theory, which, over a…

In this paper we study the smooth moduli space of closed Riemann surfaces. This smooth moduli is an infinite cover of the usual moduli space $\mathscr{M}_g$ of closed Riemann surfaces, and is identified with the Schottky space of rank $g.$…

Let $\pi: X \longrightarrow C$ be a fibration with reduced fibers over a curve $C$ and consider a polarization $H$ on the surface $X$. Let $E$ be a stable vector bundle of rank $2$ on $C$. We prove that the pullback $\pi^*E$ is a $H-$stable…

Let T -> S be a finite flat morphism of degree two between regular integral schemes of dimension at most two (and with 2 invertible), having regular branch divisor D. We establish a bijection between Azumaya quaternion algebras on T and…

We discuss the hypersurfaces of the moduli spaces of rank $2$ vector bundles on a classical Hopf surface formed by irregular bundles.

We introduce a new class of $\mathfrak{sl}_2$-triples in a complex simple Lie algebra $\mathfrak{g}$, which we call magical. Such an $\mathfrak{sl}_2$-triple canonically defines a real form and various decompositions of $\mathfrak{g}$.…

We show that the $G_2$-manifolds and certain ${\rm Spin}(7)$-manifolds are endowed with natural Riemannian twistorial structures. Along the way, the exceptional holonomy representations are reviewed and other related facts are considered.

In this paper, we regard the smooth quadric threefold $Q_{3}$ as Lagrangian Grassmannian and search for fixed rational curves of low degree in $Q_{3}$ with respect to a torus action, which is the maximal subgroup of the special linear group…

Let $(\Sigma,\tau)$ denote a Riemann surface of genus $g \geq 2$ equipped with an anti-holomorphic involution $\tau$. In this paper we study the topology of the moduli space $M(r,\xi)^\tau$ of stable Real vector bundles over $(\Sigma,\tau)$…

Two-dimensional almost-Riemannian structures are generalized Riemannian structures on surfaces for which a local orthonormal frame is given by a Lie bracket generating pair of vector fields that can become collinear. We study the relation…

We introduce the moduli space of quasi-parabolic $SL(2,\mathbb{C})$-Higgs bundles over a compact Riemann surface $\Sigma$ and consider a natural involution, studying its fixed point locus when $\Sigma$ is $\mathbb{C} \mathbb{P}^1$ and…

In this note, we describe the possible singularities on a stable surface which is in the boundary of the moduli space of surfaces isogenous to a product. Then we use the $\mathbb Q$-Gorenstein deformation theory to get some connected…

We study the Hitchin component in the space of representations of the fundamental group of a Riemann surface into a split real simple Lie group in the rank 2 case. We prove that such representations are described by a conformal structure…

We show that the Verlinde formula for moduli spaces of spin bundles on an algebraic curve gives dimensions of direct sums of spaces of theta functions over the finite set of Prym varieties of unramified double covers of the curve. We then…