Given an abstract triangulation of a torus, there is a unique point in moduli space which supports a circle packing for this triangulation. We will describe combinatorial deformations analogous to the process of conformal welding. These combinatorial deformations allow us to travel in moduli space from any packable torus to a point arbitrarily close to any other torus we choose. We also provide...

We compute the Riemannian volume of the moduli space of flat connections on a nonorientable 2-manifold, for a natural class of metrics. We also show that Witten’s volume formula for these moduli spaces may be derived using Haar measure, and we give a new proof of Witten’s volume formula for the moduli space of flat connections on a Riemann surface using Haar measure. ———————–

This paper introduces a submanifold of the moduli space of unitary representations of the fundamental group of a punctured sphere with fixed local monodromy. The submanifold is defined via products of involutions through Lagrangian subspaces. We show that the moduli space of Lagrangian representations is a Lagrangian submanifold of the moduli of unitary representations.

In this paper we describe a general method of constructing special effective divisors on various moduli spaces using the syzygies of the parametrized objects. The method can be applied to a wide range of moduli problems with the property that the coarse moduli space has canonical singularities hence pluricanonical forms extend over any desingularization of the moduli space. Here we treat the ca...

Moduli spaces of general polarized algebraic varieties are studied extensively by algebraic geometers. However, there are two classes of moduli spaces where the methods of differential geometry are equally powerful. These are the moduli spaces of curves and the moduli spaces of polarized Calabi-Yau manifolds. Both spaces are complex orbifolds. The Weil-Petersson metric is the main tool for inve...

1. Preface 1 2. The Dolbeault Moduli Space 3 2.1. Higgs bundles 3 2.2. The moduli space 8 2.3. The Hitchin-Kobayashi correspondence 13 3. The Betti Moduli Space 22 3.1. Representation varieties 22 3.2. Local systems and holomorphic connections 23 3.3. The Corlette-Donaldson theorem 27 3.4. Hyperkähler reduction 32 4. Differential Equations 34 4.1. Uniformization 34 4.2. Higher order equations 3...

This survey discusses the geometry of the moduli space of Prym varieties. Several applications of Pryms in algebraic geometry are presented. The paper begins with with a historical discussion of the life and achievements of Friedrich Prym. Topics treated in subsequent sections include singularities and Kodaira dimension of the moduli space, syzygies of Prym-canonical embedding and the geometry ...

We classify parallelizable noncommutative manifold structures on finite sets of small size in the general formalism of framed quantum manifolds and vielbeins introduced in [10]. The full moduli space is found for ≤ 3 points, and a restricted moduli space for 4 points. Generalised Levi-Civita connections and their curvatures are found for a variety of models including models of a discrete torus....

We study the geometry of the moduli space M0,n(G(2, 4), d). We consider a particular stratification of this moduli. As a consequence we compute the degree of the variety parametrizing rational ruled surfaces with a minimal directrix of degree [ d 2 ]− 1 by studying divisors in the moduli space of stable maps.

The modular trace of the normalized Hauptmodul has been extended to Galois a class invariant by Kaneko. It is an important issue search for invariants which traces have properties. crucial point in this paper that we initiate new notion, called Siegel resolvents; define resolvents as quadratic polynomials functions level 3, so they are 3 well. We construct real-valued over imaginary fields usin...