Related papers: Moduli Spaces for Dynamical Systems with Portraits

In this paper, we construct the moduli spaces of filtered $G$-local systems on curves for an arbitrary reductive group $G$ over an algebraically closed field of characteristic zero. This provides an algebraic construction for the Betti…

The moduli space of regular stable maps with values in a complex manifold admits naturally the structure of a complex orbifold. Our proof uses the methods of differential geometry rather than algebraic geometry. It is based on Hardy…

In this note, we give a new simple system of global parameters on the moduli space of rational functions, and clarify the relation to the parameters indicating location of fixed points and the indices at them. As a byproduct, we solve a…

Let $\MP_d$ denote the space of polynomials $f: \C \to \C$ of degree $d\geq 2$, modulo conjugation by $\Aut(\C)$. Using properties of polynomial trees (as introduced in [DM, math.DS/0608759]), we show that if $f_n$ is a divergent sequence…

Let $\Sigma$ be a closed surface, $G$ a compact Lie group, with Lie algebra $g$, and $\xi \colon P \to \Sigma$ a principal $G$-bundle. In earlier work we have shown that the moduli space $N(\xi)$ of central Yang- Mills connections, for…

A part of Grothendieck's program for studying the Galois group $G_{\mathbb Q}$ of the field of all algebraic numbers $\overline{\mathbb Q}$ emerged from his insight that one should lift its action upon $\overline{\mathbb Q}$ to the action…

We develop the theory of adequate moduli spaces in characteristic $p$ (and mixed characteristic) characterizing quotients by geometrically reductive group schemes.

In these lecture notes, we present a connection between the complex dynamics of a family of rational functions $f_t: \mathbb{P}^1\to \mathbb{P}^1$, parameterized by $t$ in a Riemann surface $X$, and the arithmetic dynamics of $f_t$ on…

Over a family $\mathbb X$ of genus $g$ complete curves, which gives the degeneration of a smooth curve into one with nodal singularities, we build a moduli space which is the moduli space of ${\rm SL}(n, \mathbb C)$ bundles over the generic…

We construct the moduli space of r-jets at a point of Riemannian metrics on a smooth manifold. The construction is closely related to the problem of classification of jet metrics via differential invariants. The moduli space is proved to be…

This paper provides a GIT construction of the Moduli Space of Stable Maps as a GIT quotient of the Graph Space by SL(2,C). As a corollary, we get a birational map from the 0-pointed Moduli Space to a projective variety.

We study the moduli functor of flat bundles on smooth, possibly non-proper, algebraic variety $X$ (over a field of characteristic zero). For this we introduce the notion of \emph{formal boundary} of $X$, denoted by $\partial X$, which is a…

In [arXiv:2008.04625] the authors constructed a classifying space for polystable holomorphic vector bundles on a compact K\"ahler manifold using analytic GIT theory. The aim of this article is to show that this classifying space taken in…

We prove the existence of quasi-projective coarse moduli spaces parametrising certain complete flags of subschemes of a fixed projective space $\mathbb{P}(V)$ up to projective automorphisms. The flags of subschemes being parametrised are…

Given a finite group scheme $\cG$ over an algebraically closed field $k$ of characteristic $\Char(k)=p>0$, we introduce new invariants for a $\cG$-module $M$ by associating certain morphisms $\deg^j_M : U_M \lra \Gr_d(M) \ \…

We compare the Kontsevich moduli space of genus 0 stable maps to projective space with the quasi-map space when $d=3$. More precisely, we prove that when $d=3$, the obvious birational map from the quasi-map space to the moduli space of…

In this note we prove that the moduli space of rank $2n$ symplectic instanton bundles on ${\PP^{2n+1}}$, defined from the well known monad condition, is affine. This result was not known even in the case $n=1$, where the real instanton…

Let $X$ be a compact manifold, $D$ a real elliptic operator on $X$, $G$ a Lie group, $P\to X$ a principal $G$-bundle, and ${\mathcal B}_P$ the infinite-dimensional moduli space of all connections $\nabla_P$ on $P$ modulo gauge, as a…

We study the moduli space of discrete, faithful, type-preserving representations of the modular group $\mathbf{PSL}(2,\mathbb{Z})$ into $\mathbf{PU}(3,1)$. The entire moduli space $\mathcal{M}$ is a union of…

This article investigates the two-parameter quantum matrix algebra at roots of unity. In the roots of unity setting, this algebra becomes a Polynomial Identity (PI) algebra and it is known that simple modules over such algebra are…