Related papers: 2\pi-grafting and complex projective structures wi…

We explain how we computed equations for all genus 4 curves defined of the field with 2 elements, up-to-isomorphism, and some of the data we obtained. We give descriptions also of nice models for genus 4 curves over characteristic 2 fields,…

We prove that structured vector bundles whose holonomies lie in GL(N,C), SO(N,C), or Sp(2N,C) have structured inverses. This generalizes a theorem of Simons and Sullivan.

The aim of this paper and its sequel is to introduce and classify the holonomy algebras of the projective Tractor connection. After a brief historical background, this paper presents and analyses the projective Cartan and Tractor…

We construct moduli stacks of two-dimensional mod p representations of the absolute Galois group of a p-adic local field, and relate their geometry to the weight part of Serre's conjecture for GL(2).

We study the set ${\mathcal P}_S$ consisting of all branched holomorphic projective structures on a compact Riemann surface $X$ of genus $g \geq 1$ and with a fixed branching divisor $S:= \sum_{i=1}^d n_i\cdot x_i$, where $x_i \in X$. Under…

Based on the analogies between knot theory and number theory, we study a deformation theory for SL_2-representations of knot groups, following after Mazur's deformation theory of Galois representations. Firstly, by employing the…

Let $\Gamma$ be the fundamental group of a $k$-punctured, $k \geq 0$, closed connected orientable surface of genus $g \geq 2$. We show that the character variety of the $(Q^+, Q^-)$-Anosov irreducible representations, resp. the character…

We construct analogues of Fenchel-Nielsen coordinates on an open and dense subset of the space of holonomies of branched hyperbolic structures on a closed genus-2 surface. We show that these coordinates satisfy an analogue of Wolpert's…

We prove that every discrete faithful representation of the surfcae group into SL(2,C) is the monodromy of a holomorphic connection on the trivial rank-2 vector bundle over a Riemann surface. As an application, we answer the question posed…

In this paper, we define a generalized elliptic genus of an almost complex manifold with an extra complex bundle which generalize the elliptic genus in [10]. This generalized elliptic genus is a generalized Jacobi form. By this generalized…

We give a complete list of orbifolds uniformised by discrete non-elementary two-generator subgroups of PSL(2,C) without invariant plane whose generators and their commutator have real traces.

It is proved that if $S\subset \mathbb P^N$ is a smooth projective surface and $f:S\to \mathbb P^2$ is a generic linear projection branched over a cuspidal curve $B\subset \mathbb P^2$, then the surface $S$ is determined uniquely up to an…

Springer varieties appear in both geometric representation theory and knot theory. Motivated by knot theory and categorification Khovanov provides a topological construction of $(n/2, n/2)$ Springer varieties. We extend Khovanov's…

A set of multi-homogeneous equations for the Jacobian of a genus two curve is given. The approach used is to write down affine equations for the Jacobian minus various tranlations of the Theta-divisor by [2]-division points, and then to…

We study the limits of holonomy representations of complex projective structures on a compact Riemann surface in the Morgan-Shalen compactification of the character variety. We show that the dual R-trees of the quadratic differentials…

We construct a modular desingularisation of $\overline{\mathcal{M}}_{2,n}(\mathbb{P}^r,d)^{\text{main}}$. The geometry of Gorenstein singularities of genus two leads us to consider maps from prestable admissible covers: with this enhanced…

Two-dimensional sigma-models describing superstrings propagating on manifolds of special holonomy are characterized by symmetries related to covariantly constant forms that these manifolds hold, which are generally non-linear and close in a…

We investigate the Lawson genus $2$ surface by methods from integrable system theory. We prove that the associated family of flat connections comes from a family of flat connections on a $4-$punctured sphere. We describe the symmetries of…

Let $K/F$ be a quadratic extension of $p$-adic fields, $\sigma$ the nontrivial element of the Galois group of $K$ over $F$, and $\pi$ a quasi-square-integrable representation of $GL(n,K)$. Denoting by $\pi^{\vee}$ the smooth contragredient…

In a recent paper [J. Combin. Theory Ser. B}, 113 (2015), pp. 1-17], the authors have extended the concept of quadrangulation of a surface to higher dimension, and showed that every quadrangulation of the $n$-dimensional projective space…