Related papers: Artin-Schreier Root Stacks

It is common in stability analysis to linearize a system and investigate the spectrum of the Jacobian matrix. This approach faces the challenge of determining the matrix spectrum when the coefficients depend on parameters or when the…

We give an explicit finite-dimensional model for the derived moduli stack of flat connections on $\mathbb{C}^k$ with logarithmic singularities along a weighted homogeneous Saito free divisor. We investigate in detail the case of plane…

We establish a formula for computing the unramified Brauer group of tame conic bundle threefolds in characteristic 2. The formula depends on the arrangement and residue double covers of the discriminant components, the latter being governed…

We construct a rational homotopy pullback decomposition for variants of the classifying space of the group of homeomorphisms for a large class of manifolds. This has various applications, including a rational section of the stabilisation…

For proper stacks, unlike schemes, there is a distinction between rational and integral points. Moreover, rational points have extra automorphism groups. We show that these distinctions exactly account for the lower order main terms…

We determine the splitting (isomorphism) type of the normal bundle of a generic genus-0 curve with 1 or 2 components in any projective space, as well as the (sometimes nontrivial) way the bundle deforms locally with a general deformation of…

For a smooth surface X over an algebraically closed field of positive characteristic, we consider the ramification of an Artin-Schreier extension of X. A ramification at a point of codimension 1 of X is understood by the Swan conductor. A…

We study the compactification of the moduli space of a certain class of rank-two irregular connections on the Riemann sphere, presenting one double pole and two simple poles. To construct the compactification explicitly, we identify a class…

Let $p \geq 5$ be a prime number and let $G = SL_2(\mathbb{Q}_p)$. Let $\Xi$ = Spec$(Z)$ denote the spectrum of the centre $Z$ of the pro-$p$ Iwahori Hecke algebra of $G$ with coefficients in a field $k$ of characteristic $p$. Let…

For a family of principal bundles with a reductive structure group on a family of curves in characteristic zero, it is known that the Harder Narasimhan type of its restriction to each fiber varies semicontinuously over the parameter scheme…

We continue the study of a general class of spaces of 0-cycles on a manifold defined and begun by Farb-Wolfson-Wood. Using work of Gadish on linear subspace arrangements, we obtain representation stability for the cohomology of the ordered…

We construct inductively an equivariant compactification of the algebraic group ${\mathbb W}_n$ of Witt vectors of finite length over a field of characteristic $p>0$. We obtain smooth projective rational varieties $\bar{\mathbb W}_n$,…

In this note, we introduce the notion of an unramified strongly cyclic covering for a cyclic curve, a class that has similar properties to, and contains, unramified double covers of hyperelliptic curves. We determine several of their basic…

The present work completes the classification of the compact Riemann surfaces of genus g with an analytic automorphism of order p (prime number) and p > g. More precisely, we construct a parameteriza- tion space for them, we compute their…

We study branched covers of curves with specified ramification points, under a notion of equivalence derived from linear series. In characteristic 0, no non-constant families of covers with fixed ramification points exist. In positive…

The notion of $m/\Gamma$-pointed stable curves is introduced. It should be viewed as a generalization of the notion of m-pointed stable curves of a given genus, where the labels of the marked points are only determined up to the action of a…

Let $X=\overline{X}-D$ be a smooth quasi-projective curve. In arXiv:2110.12300 we constructed a Deligne-Hitchin modui space with Hecke gauge groupoid for connections of rank $2$. We extend this construction to the case of any rank $r$,…

We propose a novel tree-like curvilinear structure reconstruction algorithm based on supervised learning and graph theory. In this work we analyze image patches to obtain the local major orientations and the rankings that correspond to the…

We give criteria for certain morphisms from an algebraic stack to a (not necessarily algebraic) stack to admit an (appropriately defined) scheme-theoretic image. We apply our criteria to show that certain natural moduli stacks of local…

We study the Simpson moduli space of semi-stable sheaves on the complex projective plane that have dimension 1, multiplicity 6 and Euler characteristic 2. We describe concretely these sheaves as cokernels of morphisms of locally free…