Related papers: On cyclic groups covers of the projective line

We study K3 surfaces with complex multiplication following the classical work of Shimura on CM abelian varieties. After we translate the problem in terms of the arithmetic of the CM field and its id\`{e}les, we proceed to study some abelian…

We study a notion of curvature for finitely generated groups which serves as a role of Ricci curvature for Riemannian manifolds. We prove an analog of Cheeger-Gromoll splitting theorem. As a consequence, we give a geometric characterization…

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…

The paper contains a general construction which produces new examples of non simply-connected smooth projective surfaces. We analyze the resulting surfaces and their fundamental groups. Many of these fundamental groups are expected to be…

Let $X$ be a smooth complex projective algebraic variety. Let $\mathcal{G}$ be a $G$-banded gerbe with $G$ a finite abelian group. We prove an exact formula expressing genus $g$ orbifold Gromov-Witten invariants of $\mathcal{G}$ in terms of…

Given a Galois cover of curves over $\mathbb{F}_p$, we relate the $p$-adic valuation of epsilon constants appearing in functional equations of Artin L-functions to an equivariant Euler characteristic. Our main theorem generalises a result…

We describe a new construction of families of Galois coverings of the line using basic properties of configuration spaces, covering theory, and the Grauert-Remmert Extension Theorem. Our construction provides an alternative to a previous…

We compute a presentation of the fundamental group of a higher-rank graph using a coloured graph description of higher-rank graphs developed by the third author. We compute the fundamental groups of several examples from the literature. Our…

Let $S_g$ be the closed oriented surface of genus $g \geq 0$, and let $\mathrm{Mod}(S_g)$ be the mapping class group of $S_g$. For $g\geq 2$, we develop an algorithm to obtain a finite generating set for the liftable mapping class group…

For an algebraically closed field K, let G be a finite abelian group of K-linear automorphisms of a finite-dimensional path algebra KQ of a quiver Q. Under certain assumptions on the action of G, we show the existence of a certain kind of…

We determine the Picard number and the Ulrich complexity of general bidouble covers of the projective plane, providing the first systematic study of Ulrich bundles on non-cyclic abelian covers. For a bidouble plane branched along three…

Applying geometric methods of $2$-dimensional cell complex theory, we construct a Galois covering of a bimodule problem satisfying some structure, triangularity and finiteness conditions in order to describe the objects of finite…

We study the arithmetic of curves and Jacobians endowed with the action of a finite group $G$. This includes a study of the basic properties, as $G$-modules, of their $\ell$-adic representations, Selmer groups, rational points and…

The Gelfand - Na\u{i}mark theorem supplies the one to one correspondence between commutative $C^*$-algebras and locally compact Hausdorff spaces. So any noncommutative $C^*$-algebra can be regarded as a generalization of a topological…

Let $K$ be a field whose characteristic is prime to a fixed integer $n$ with $\mu_n \subset K$, and choose $\omega \in \mu_n$ a primitive $n$th root of unity. Denote the absolute Galois group of $K$ by $\operatorname{Gal}(K)$, and the…

In this work we use arithmetic, geometric, and combinatorial techniques to compute the cohomology of Weil divisors of a special class of normal surfaces, the so-called rational ruled toric surfaces. These computations are used to study the…

Given a genus two curve $X: y^2 = x^5 + a x^3 + b x^2 + c x + d$, we give an explicit parametrization of all other such curves $Y$ with a specified symplectic isomorphism on three-torsion of Jacobians $\mbox{Jac}(X)[3] \cong…

Let $\ell$ be a rational prime and $k$ a number field. Given a superelliptic curve $C/k$ of $\ell$-power degree, we describe the field generated by the $\ell$-power torsion of the Jacobian variety in terms of the branch set and reduction…

We extend to compact K\"ahler manifolds some classical results on linear representation of fundamental groups of complex projective manifolds. Our approach based on an interversion lemma for fibrations with tori versus general type…

For the cyclic group $C_2$ we give a complete description of the derived category of perfect complexes of modules over the constant Mackey ring $\underline{\mathbb{Z}/\ell}$, for $\ell$ a prime. This is fairly simple for $\ell$ odd, but for…