Related papers: Moduli of double EPW-sextics

Let $G$ be a real reductive Lie group, and $H^{\mathbb{C}}$ the complexification of its maximal compact subgroup $H\subset G$. We consider classes of semistable $G$-Higgs bundles over a Riemann surface $X$ of genus $g\geq2$ whose underlying…

We show that the moduli space of rational elliptic surfaces admitting a section is locally a complex hyperbolic variety of dimension eight. We compare its Satake-Baily-Borel compactification with a compactification obtained by means of…

The gauged sigma model with target $\mathbb{P}^1$, defined on a Riemann surface $\Sigma$, supports static solutions in which $k_+$ vortices coexist in stable equilibrium with $k_-$ antivortices. Their moduli space is a noncompact complex…

Let $(X, \omega)$ be a compact symplectic manifold and $L$ be a Lagrangian submanifold. Suppose $(X, L)$ has a Hamiltonian $S^1$ action with moment map $\mu$. Take an invariant $\omega$-compatible almost complex structure, we consider…

In this article, we study the topology and bifurcations of the moduli space $\mathcal{M}_3$ of cubic Newton maps. It's a subspace of the moduli space of cubic rational maps, carrying the Riemann orbifold structure $(\mathbb{\widehat{C}},…

We study the moduli space of Gieseker semi-stable sheaves on the complex projective plane supported on sextic curves and having Euler characteristic one. We determine locally free resolutions of length one for all such sheaves. We decompose…

We construct a quantization of the moduli space $\mathcal{GH}_\Lambda(S\times\mathbb{R})$ of maximal globally hyperbolic Lorentzian metrics on $S\times \mathbb{R}$ with constant sectional curvature $\Lambda$, for a punctured surface $S$.…

Coassociative 4-folds are a particular class of 4-dimensional submanifolds which are defined in a 7-dimensional manifold M with a G_2 structure given by a `positive' differential 3-form, sometimes called G_2-form. Assuming that a G_2-form…

We study the moduli space of M-theories compactified on G_2 manifolds which are asymptotic to a cone over quotients of S^3 x S^3. We show that the moduli space is composed of several components, each of which interpolates smoothly among…

For a smooth cubic fourfold Y, we study the moduli space M of semistable objects of Mukai vector $2\lambda_1+2\lambda_2$ in the Kuznetsov component of Y. We show that with a certain choice of stability conditions, M admits a symplectic…

Let G be a linear algebraic group, P be a parabolic subgroup of G and \beta be a cycle of dimension 1 in the Chow group of the quotient G/P. Using geometric arguments and Borel's fixed point theorem, we prove that the moduli space…

Let $G$ be a simple complex Lie group, $\alg{g}$ be its Lie algebra, $K$ be a maximal compact form of $G$ and $\alg{k}$ be a Lie algebra of $K$. We denote by $X\rightarrow \overline{X}$ the anti-involution of $\alg{g}$ which singles out the…

Let $\mathcal C$ be a smooth irreducible projective curve over the complex numbers and let $G$ be a simple simply-connected complex algebraic group. Let $\mathfrak M=\mathfrak M(G,\mathcal C)$ be the moduli space of semistable principal…

Consider the moduli space M^0 of arrangements of n hyperplanes in general position in projective (r-1)-space. When r=2 the space has a compactification given by the moduli space of stable curves of genus 0 with n marked points. In higher…

Let X be a nonsingular projective algebraic curve of genus g\ge3. We consider the moduli space M of stable bundles of fixed determinant with rank n and degree d coprime and d>n(2g-2). There is a universal bundle on XxM and we consider the…

Eisenbud Popescu and Walter have constructed certain special 4-dimensional sextic hypersurfaces as Lagrangian degeneracy loci. We prove that the natural double cover of a generic EPW-sextic is a deformation of the Hilbert square of a…

Let $X$ be a compact Riemann surface of genus $g \geq 3$ and $S$ a finite subset of $X$. Let $\xi$ be fixed a holomorphic line bundle over $X$ of degree $d$. Let $\mathcal{M}_{pc}(r, d, \alpha)$ (respectively, $\mathcal{M}_{pc}(r, \alpha,…

We establish an implication between two long-standing open problems in complex dynamics. The roots of the $n$-th Gleason polynomial $G_n\in\mathbb{Q}[c]$ comprise the $0$-dimensional moduli space of quadratic polynomials with an…

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…

In this paper we consider a dimensional reduction of slightly modified Seiberg-Witten equations, the modification being a different choice of the Pauli matrices which go into defining the equations. We get interesting equations with a Higgs…