Related papers: Characterizing covers via simple closed curves

A family of proper smooth curves of genus $\geq 2$, parametrised by an open dense subset $U$ of a normal variety $S$, extends to $S$ if the natural map $\pi_1(U) \to \pi_1(S)$ on fundamental groups is an isomorphism. The criterion of this…

We classify minimal complex surfaces of general type with $p_g=q=3$. More precisely, we show that such a surface is either the symmetric product of a curve of genus 3 or a free $\Z_2-$quotient of the product of a curve of genus 2 and a…

For conic bundles on a smooth variety (over a field of characteristic $\ne 2$) which degenerate into pairs of distinct lines over geometric points of a smooth divisor, we prove a theorem which relates the Brauer class of the non-degenerate…

We classify all the surfaces with p_g = q = 0 which admit an unramified covering which is isomorphic to a product of curves. Beyond the trivial case \PP^1 x \PP^1 we find 17 families which we explicitly describe. We reduce the problem to a…

We sharpen the two main tools used to treat the compactified Jacobian of a singular curve: Abel maps and presentation schemes. First we prove a smoothness theorem for bigraded Abel maps. Second we study the two complementary filtrations…

A curve over a field of characteristic $p$ is called ordinary if the $p$-torsion of its Jacobian as large as possible, that is, an $\mathbb{F}_p$ vector space of dimension equal to its genus. In this paper we consider the following…

Assume that $X$ and $Y$ are arithmetic schemes, i.e., integral schemes of finite types over $Spec(\mathbb{Z})$. Then $X$ is said to be quasi-galois closed over $Y$ if $X$ has a unique conjugate over $Y$ in some certain algebraically closed…

This paper investigates Galois branched covers of the open $p$-adic disc and their reductions to characteristic $p$. Using the field of norms functor of Fontaine and Wintenberger, we show that the special fiber of a Galois cover is…

Special covers are metacyclic covers of the projective line, with Galois group of order pm, which have a specific type of bad reduction to characteristic p. Such covers arise in the study of the arithmetic of Galois covers of the projective…

Let $Y$ be a smooth curve embedded in a complex projective manifold $X$ of dimension $n\geq 2$ with ample normal bundle $N_{Y|X}$. For every $p\geq 0$ let $\alpha_p$ denote the natural restriction maps $\Pic(X)\to\Pic(Y(p))$, where $Y(p)$…

We show that algebraic analogues of universal group covers, surjective group homomorphisms from a $\mathbb{Q}$-vector space to $F^{\times}$ with "standard kernel", are determined up to isomorphism of the algebraic structure by the…

Let $X$ be a minimal surface of general type over an algebraically closed field $\mathbf{k}$ of $\mathrm{char}.(\mathbf{k})=p\ge 0$. If the Albanese morphism $a_X:X\to \mathrm{Alb}_X$ is generically finite onto its image, we formulate a…

Let X and Y be curves over a finite field. In this article we explore methods to determine whether there is a rational map from Y to X by considering L-functions of certain covers of X and Y and propose a specific family of covers to…

Our goal is to give a purely algebraic characterization of finite abelian Galois covers of a complete, irreducible, non-singular curve $X$ over an algebraically closed field $\k$. To achieve this, we make use of the Galois theory of…

This article describes the geometry of isomorphisms between complements of geometrically irreducible closed curves in the affine plane $\mathbb{A}^2$, over an arbitrary field, which do not extend to an automorphism of $\mathbb{A}^2$. We…

We completely determine finite abelian regular branched covers of the 2-sphere $S^2$ with the property that each homeomorphism of $S^2$ preserving the branching set can be lifted.

We prove that a smooth projective surface $S$ over an algebraically closed field of characteristic $p>3$ is birational to an abelian surface if $P_1(S)=P_4(S)=1$ and $h^1(S,\mathcal{O}_S)=2$.

Consider a finite, regular cover $Y\to X$ of finite graphs, with associated deck group $G$. We relate the topology of the cover to the structure of $H_1(Y;\mathbb{C})$ as a $G$-representation. A central object in this study is the {\em…

Let E be a rank two vector bundle on a scheme X. The following three structures are shown to be equivalent : a) A primitive quadratic map q: E --> L, with values in an invertible module L. b) A double covering f: Y --> X endowed with an…

Given a normed plane $\mathcal{P}$, we call $\mathcal{P}$-cycloids the planar curves which are homothetic to their double $\mathcal{P}$-evolutes. It turns out that the radius of curvature and the support function of a $\mathcal{P}$-cycloid…